Apparatus and method for encoding/decoding transport format combination indicator in CDMA mobile communication system

ABSTRACT

An apparatus and method for encoding/decoding a transport format combination indicator (TFCI) in a CDMA mobile communication system. In the TFCI encoding apparatus, a one-bit generator generates a sequence having the same symbols. A basis orthogonal sequence generator generates a plurality of basis orthogonal sequences. A basis mask sequence generator generates a plurality of basis mask sequences. An operation unit receives TFCI bits that are divided into a first information part representing biorthogonal sequence conversion, a second information part representing orthogonal sequence conversion, and a third information part representing mask sequence conversion and combines an orthogonal sequence selected from the basis orthogonal sequence based on the second information, a biorthogonal sequence obtained by combining the selected orthogonal sequence with the same symbols selected based on the first information part, and a mask sequence selected based on the biorthogonal sequence and the third information part, thereby generating a TFCI sequence.

PRIORITY

This application is a continuation of application Ser. No. 09/611,069,filed Jul. 6, 2000, which claims priority under 35 U.S.C. § 119 to anapplication entitled “Apparatus And Method For Encoding/DecodingTransport Format Combination Indicator In CDMA Mobile CommunicationSystem” filed in the Korean Intellectual Property Office on Jul. 6, 1999and assigned Serial No. 1999-27932, the contents of each of which arehereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to an information transmittingapparatus and method in an IMT 2000 system, and in particular, to anapparatus and method for transmitting a transport format combinationindicator (TFCI).

2. Description of the Related Art

A CDMA mobile communication system (hereinafter, referred to as an IMT2000 system) generally transmits frames that provide a voice service, animage service, a character service on a physical channel such as adedicated physical data channel (DPDCH) at a fixed or variable datarate. In the case where the data frames which include that sort ofservices are transmitted at a fixed data rate, there is no need toinform a receiver of the spreading rate of each data frame. On the otherhand, if the data frames are transmitted at a variable data rate, whichimplies that each data frame has a different data rate, a transmittershould inform the receiver of the spreading rate of each data framedetermined by its data rate. A data rate is proportional to a datatransmission rate and the data transmission rate is inverselyproportional to a spreading rate in a general IMT 2000 system.

For transmission of data frames at a variable data rate, a TFCI field ofa DPCCH informs a receiver of the data rate of the current serviceframe. The TFCI field includes a TFCI indicating a lot of informationincluding the data rate of a service frame. The TFCI is information thathelps a voice or data service to reliably be provided.

FIGS. 1A to 1D illustrate examples of applications of a TFCI. FIG. 1Aillustrates application of the TFCI to an uplink DPDCH and an uplinkdedicated physical control channel (DPCCH). FIG. 1B illustratesapplication of the TFCI to a random access channel (RACH). FIG. 1Cillustrates application of the TFCI to a downlink DPDCH and a downlinkDPCCH. FIG. 1D illustrates application of the TFCI to a secondary commoncontrol physical channel (SCCPCH).

Referring to FIGS. 1A to 1D, one frame is comprised of 16 slots and eachslot has a TFCI field. Thus, one frame includes 16 TFCI fields. A TFCIfield includes N_(TFCI) bits and a TFCI generally has 32 bits in aframe. To transmit the 32-bit TFCI in one frame, 2 TFCI bits can beassigned to each of the 16 slots (T_(slot)=0.625 ms).

FIG. 2 is a block diagram of a base station transmitter in a general IMT2000 system.

Referring to FIG. 2, multipliers 211, 231, and 232 multiply inputsignals by gain coefficients G₁, G₃, and G₅. Multipliers 221, 241, and242 multiply TFCI codewords (TFCI code symbols) received fromcorresponding TFCI encoders by gain coefficients G₂, G₄, and G₆. Thegain coefficients G₁ to G₆ may have different values according toservice types or handover situations. The input signals include pilotsand power control signals (TPCs) of a DPCCH and a DPDCH data. Amultiplexer 212 inserts 32 bit TFCI code symbols(TFCI codeword) receivedfrom the multiplier 221 into the TFCI fields as shown in FIG 1C. Amultiplexer 242 inserts 32-bit TFCI code symbols received from themultiplier 241 into the TFCI fields. A multiplexer 252 inserts 32-bitTFCI code symbols received from the multiplier 242 into the TFCI fields.Insertion of TFCI code symbols into TFCI fields is shown in FIGS. 1A to1D. The 32 code symbols are obtained by encoding TFCI bits(informationbits) that define the data rate of a data signal on a corresponding datachannel. 1^(st), 2^(nd), and 3^(rd) serial to parallel converters (S/Ps)213, 233, and 234 separate the outputs of the multiplexers 212, 242, and252 into I channels and Q channels. Multipliers 214, 222, and 235 to 238multiply the outputs of the S/Ps 213, 233, and 234 by channelizationcodes C_(ch1), C_(ch2), and C_(ch3). The channelization codes areorthogonal codes. A first summer 215 sums the outputs of the multipliers214, 235, and 237 and generates an I channel signal and a second summer223 sums the outputs of the multipliers 222, 236, and 238 and generatesa Q channel signal. A phase shifter 224 shifts the phase of the Qchannel signal received from the second summer 223 by 90°. A summer 216adds the outputs of the first summer 215 and the phase shifter 224 andgenerates a complex signal I+jQ. A multiplier 217 scrambles the complexsignal with a complex PN sequence C_(scramb) assigned to the basestation. A signal processor(S/P) 218 separates the scrambled signal intoan I channel and a Q channel. Low-pass filters (LPFs) 219 and 225 limitsthe bandwidths of the I channel and Q channel signals received from theS/P 218 by low-pass-filtering. Multipliers 220 and 226 multiply theoutputs of the LPFs 219 and 225 by carriers cos(2πf_(c)t) andsin(2πf_(c)t), respectively, thereby transforming the outputs of theLPFs 219 and 225 to an RF (Radio Frequency) band. A summer 227 sums theRF I channel and Q channel signals.

FIG. 3 is a block diagram of a mobile station transmitter in the generalIMT 2000 system.

Referring to FIG. 3, multipliers 311, 321, and 323 multiplycorresponding signals by channelization codes C_(ch1), C_(ch2), andC_(ch3). Signals 1, 2, 3 are first, second and third DPDCH signal. Aninput signal 4 includes pilots and TPCs of a DPCCH.TFCI information bitsare encoded into 32 bit TFCI code symbols by a TFCI encoder 309. Amultiplier 310 inserts a 32 bit TFCI code symbols into the signal 4 asshown in FIG. 1A. A multiplier 325 multiplies a DPCCH signal whichinclude TFCI code symbol received from the multiplier 310 by achannelization code C_(ch4). The channelization codes C_(ch1) to C_(ch4)are orthogonal codes. The 32 TFCI code symbols are obtained by encodingTFCI information bits that define the data rate of the DPDCH signals.Multipliers 312, 322, 324, and 326 multiply the outputs of themultipliers 311, 321, 323, and 325 by gain coefficients G₁to G₄,respectably. The gain coefficients G₁ to G₄ may have different values. Afirst summer 313 generates an I channel signal by adding the outputs ofthe multipliers 312 and 322. A second summer 327 generates a Q channelsignal by adding the outputs of the multipliers 324 and 326. A phaseshifter 328 shifts the phase of the Q channel signal received from thesecond summer 327 by 90°. A summer 314 adds the outputs of the firstsummer 313 and the phase shifter 328 and generates a complex signalI+jQ. A multiplier 315 scrambles the complex signal with a PN sequenceC_(scramb) assigned to a base station. An S/P 329 divides the scrambledsignal into an I channel and a Q channel. LPFs 316 and 330low-pass-filter the I channel and Q channel signals received from theS/P 329 and generate signals with limited bandwidths. Multipliers 317and 331 multiply the outputs of the LPFs 316 and 330 by carrierscos(2πf_(c)t) and sin(2πf_(c)t), respectively, thereby transforming theoutputs of the LPFs 316 and 330 to an RF band. A summer 318 sums the RFI channel and Q channel signals.

TFCIs are categorized into a basic TFCI and an extended TFCI. The basicTFCI represents 1 to 64 different information including the data ratesof corresponding data channels using 6 TFCI information bits, whereasthe extended TFCI represents 1 to 128, 1 to 256, 1 to 512, or 1 to 1024different information using 7, 8, 9 or 10 TFCI information bits. Theextended TFCI has been suggested to satisfy the requirement of the IMT2000 system for more various services. TFCI bits are essential for areceiver to receive data frames received from a transmitter. That is thereason why unreliable transmission of the TFCI information bits due totransmission errors lead to wrong interpretation of the frames in thereceiver. Therefore, the transmitter encodes the TFCI bits with an errorcorrecting code prior to transmission so that the receiver can correctpossibly generated errors in the TFCI.

FIG. 4A conceptionally illustrates a basic TFCI bits encoding structurein a conventional IMT 2000 system and FIG. 4B is an exemplary encodingtable applied to a biorthogonal encoder shown in FIG. 4A. As statedabove, the basic TFCI has 6 TFCI bits (hereinafter, referred to as basicTFCI bits) that indicate 1 to 64 different information.

Referring to FIGS. 4A and 4B, a biorthogonal encoder 402 receives basicTFCI bits and outputs 32 coded symbols(TFCI codeword or TFCI codesymbol). The basic TFCI is basically expressed in 6 bits. Therefore, inthe case where a basic TFCI bits of less than 6 bits are applied to thebiorthogonal encoder 402, 0s are added to the left end, i.e., MSB (MostSignificant Bit) of the basic TFCI bits to increase the number of thebasic TFCI bits to 6. The biorthogonal encoder 402has a predeterminedencoding table as shown in FIG. 4B to output 32 coded symbols for theinput of the 6 basic TFCI bits. As shown in FIG. 4B, the encoding tablelists 32(32-symbol) orthogonal codewords c_(32.1) to c_(32.32) and 32biorthogonal codewords {overscore (c_(32.1))} to {overscore (c_(32.32))}that are the complements of the codewords c_(32.1) to c_(32.32). If theLSB (Least Significant Bit) of the basic TFCI is 1, the biorthogonalencoder 402 selects out of the 32 biorthogonal codewords. If the LSB is0, the biorthogonal encoder 402 selects out of the 32 orthogonalcodewords. One of the selected orthogonal codewords or biorthogonalcodewords is then selected based on the other TFCI bits.

A TFCI codeword should have powerful error correction capability asstated before. The error correction capability of binary linear codesdepends on the minimum distance (dmin) between the binary linear codes.A minimum distance for optimal binary linear codes is described in “AnUpdated Table of Minimum-Distance Bounds for Binary Linear Codes”, A. E.Brouwer and Tom Verhoeff, IEEE Transactions on Information Theory, vol.39, No. 2, March 1993 (hereinafter, referred to as reference 1).

Reference 1 gives 16 as a minimum distance for binary linear codes bywhich 32 bits are output for the input of 6 bits. TFCI codewords outputfrom the biorthogonal encoder 402 has a minimum distance of 16, whichimplies that the TFCI codewords are optimal codes.

FIG. 5A conceptionally illustrates an extended TFCI bits encodingstructure in the conventional IMT 2000 system, FIG. 5B is an exemplaryalgorithm of distributing TFCI bits in a controller shown in FIG. 5A,and FIG. 5C illustrates an exemplary encoding table applied tobiorthogonal encoders shown in FIG. 5A. An extended TFCI is also definedby the number of TFCI bits. That is, the extended TFCI includes 7, 8, 9or 10 TFCI bits (hereinafter, referred to as extended TFCI bits) thatrepresent 1 to 128, 1 to 256, 1 to 512, or 1 to 1024 differentinformation, as stated before.

Referring to FIGS. 5A, 5B, and 5C, a controller 500 divides TFCI bitsinto two halves. For example, for the input of 10 extended TFCI bits,the controller 500 outputs the first half of the extended TFCI as firstTFCI bits (word 1) and the last half as second TFCI bits (word 2). Theextended TFCI are basically expressed in 10 bits. Therefore, in the casewhere an extended TFCI bits of less than 10 bits are input, thecontroller 500 adds 0s to the MSB of the extended TFCI bits to representthe extended TFCI in 10 bits. Then, the controller 500 divides the 10extended TFCI bits into word 1 and word 2. Word 1 and word 2 are fed tobiorthogonal encoders 502 and 504, respectively. A method of separatingthe extended TFCI bits a₁ to a₁₀ into word 1 and word 2 is illustratedin FIG. 5B.

The biorthogonal encoder 502 generates a first TFCI codeword having 16symbols by encoding word 1 received from the controller 500. Thebiorthogonal encoder 504 generates a second TFCI codeword having 16symbols by encoding word 2 received from the controller 500. Thebiorthogonal encoders 502 and 504 have predetermined encoding tables tooutput the 16-symbol TFCI codewords for the two 5-bit TFCI inputs (word1 and word 2). An exemplary encoding table is illustrated in FIG. 5C. Asshown in FIG. 5C, the encoding table lists 16 orthogonal codewords oflength 16 bits c_(16.1) to c_(16.16) and biorthogonal codewords{overscore (c_(16.1))} to {overscore (c_(16.16))} that are thecomplements of the 16 orthogonal codewords. If the LSB of 5 TFCI bits is1, a biorthogonal encoder (502 or 504) selects the 16 biorthogonalcodewords. If the LSB is 0, the biorthogonal encoder selects the 16orthogonal codewords. Then, the biorthogonal encoder selects one of theselected orthogonal codewords or biorthogonal codewords based on theother TFCI bits and outputs the selected codeword as the first or secondTFCI codeword.

A multiplexer 510 multiplexes the first and second TFCI codewords to afinal 32-symbol TFCI codeword.

Upon receipt of the 32-symbol TFCI codeword, a receiver decodes the TFCIcodeword separately in halves (word 1 and word 2) and obtains 10 TFCIbits by combining the two decoded 5-bit TFCI halves. In this situation,a possible error even in one of the decoded 5-bit TFCI output duringdecoding leads to an error over the 10 TFCI bits.

An extended TFCI codeword also should have a powerful error correctioncapability. To do so, the extended TFCI codeword should have the minimumdistance as suggested in reference 1.

In consideration of the number 10 of extended TFCI bits and the number32 of the symbols of a TFCI codeword, reference 1 gives 12 as a minimumdistance for an optimal code. Yet, a TFCI codeword output from thestructure shown in FIG. SA has a minimum distance of 8 because an errorin at least one of word 1 and word 2 during decoding results in an errorin the whole 10 TFCI bits. That is, although extended TFCI bits areencoded separately in halves, a minimum distance between final TFCIcodewords is equal to a minimum distance 8 between codeword outputs ofthe biorthogonal encoders 502 and 504.

Therefore, a TFCI codeword transmitted from the encoding structure shownin FIG. 5A is not optimal, which may increase an error probability ofTFCI bits in the same radio channel environment. With the increase ofthe TFCI bit error probability, the receiver misjudges the data rate ofreceived data frames and decodes the data frames with an increased errorrate, thereby decreasing the efficiency of the IMT 2000 system.

According to the conventional technology, separate hardware structuresare required to support the basic TFCI and the extended TFCI. As aresult, constraints are imposed on implementation of an IMT 2000 systemin terms of cost and system size.

SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to provide anapparatus and method for encoding an extended TFCI in an IMT 2000system.

It is also an object of the present invention to provide an apparatusand method for encoding a basic TFCI and an extended TFCI compatibly inan IMT 2000 system.

It is another object of the present invention to provide an apparatusand method for decoding an extended TFCI in an IMT 2000 system.

It is still another object of the present invention to provide anapparatus and method for decoding a basic TFCI and an extended TFCIcompatibly in an IMT 2000 system.

It is yet another object of the present invention to provide anapparatus and method for generating an optimal code by encoding anextended TFCI in an IMT 2000 system.

It is a further object of the present invention to provide a method ofgenerating mask sequences for use in encoding/decoding an extended TFCIin an IMT 2000 system.

To achieve the above objects, there is provided a TFCI encoding/decodingapparatus and method in a CDMA mobile communication system. In the TFCIencoding apparatus, a one-bit generator generates a sequence having thesame symbols. A basis orthogonal sequence generator generates aplurality of basis orthogonal sequences. A basis mask sequence generatorgenerates a plurality of basis mask sequences. An operation unitreceives TFCI bits that are divided into a 1^(st) information partrepresenting biorthogonal sequence conversion, a 2^(nd) information partrepresenting orthogonal sequence conversion, and a 3^(rd) informationpart representing mask sequence conversion and combines an orthogonalsequence selected from the basis orthogonal sequence based on the 2^(nd)information, a biorthogonal sequence obtained by combining the selectedorthogonal sequence with the same symbols selected based on the 1^(st)information part, and a mask sequence selected based on the biorthogonalcode sequence and the 3^(rd) information part, thereby generating a TFCIsequence.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will become more apparent from the following detaileddescription when taken in conjunction with the accompanying drawings inwhich:

FIGS. 1A to 1D illustrate exemplary applications of a TFCI to channelframes in a general IMT 2000 system;

FIG. 2 is a block diagram of a base station transmitter in the generalIMT 2000 system;

FIG. 3 is a block diagram of a mobile station transmitter in the generalIMT 2000 system;

FIG. 4A conceptionally illustrates a basic TFCI encoding structure in aconventional IMT 2000 system;

FIG. 4B is an example of an encoding table used in a biorthogonalencoder shown in FIG. 4A;

FIG. 5A conceptionally illustrates an extended TFCI encoding structurein the conventional IMT 2000 system;

FIG. 5B is an example of an algorithm of distributing TFCI bits in acontroller shown in FIG. 5A;

FIG. 5C is an example of an encoding table used in biorthogonal encodersshown in FIG. 5A;

FIG. 6 conceptionally illustrates a TFCI encoding structure in an IMT2000 system according to the present invention;

FIG. 7 is a flowchart illustrating an embodiment of a mask sequencegenerating procedure for TFCI encoding in the IMT 2000 system accordingto the present invention;

FIG. 8 is a block diagram of an embodiment of a TFCI encoding apparatusin the IMT 2000 system according to the present invention;

FIG. 9 is a block diagram of an embodiment of a TFCI decoding apparatusin the IMT 2000 system according to the present invention;

FIG. 10 is a flowchart illustrating a control operation of a correlationcomparator shown in FIG.9;

FIG. 11 is a flowchart illustrating an embodiment of a TFCI encodingprocedure in the IMT 2000 system according to the present invention;

FIG. 12 is a flowchart illustrating another embodiment of the TFCIencoding procedure in the IMT 2000 system according to the presentinvention;

FIG. 13 illustrates an embodiment of the structures of orthogonalsequences and mask sequences determined by a TFCI according to thepresent invention;

FIG. 14 is a block diagram of another embodiment of the TFCI encodingapparatus in the IMT 2000 system according to the present invention;

FIG. 15 is a block diagram of another embodiment of the TFCI decodingapparatus in the IMT 2000 system according to the present invention;

FIG. 16 is a flowchart illustrating another embodiment of the TFCIencoding procedure in the IMT 2000 system according to the presentinvention; and

FIG. 17 is a block diagram of a third embodiment of the TFCI decodingapparatus in the IMT 2000 system according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will be described hereinbelow with reference to the accompanying drawings. In the followingdescription, well-known functions or constructions are not described indetail since they would obscure the invention in unnecessary detail.

The present invention is directed to a TFCI encoding concept ofoutputting final code symbols (a TFCI codeword) by adding first codesymbols (a first TFCI codeword) resulting from first TFCI bits andsecond code symbols (a second TFCI codeword) resulting from second TFCIbits in an IMT 2000 system. The TFCI encoding concept is shown in FIG.6. Here, a biorthogonal sequence and a mask sequence are given as thefirst TFCI codeword and the second TFCI codeword, respectively.

Referring to FIG. 6, TFCI bits are separated into the first TFCI bitsand the second TFCI bits. A mask sequence generator 602 generates apredetermined mask sequence by encoding the second TFCI bits and abiorthogonal sequence generator 604 generates a predeterminedbiorthogonal sequence by encoding the first TFCI bits. An adder 610 addsthe mask sequence and the biorthogonal sequence and outputs final codesymbols (a TFCI codeword). The mask sequence generator 602 may have anencoding table that lists mask sequences for all possible second TFCIbits. The biorthogonal sequence generator 604 may also have an encodingtable that lists biorthogonal sequences for all possible first TFCIbits.

As described above, mask sequences and a mask sequence generating methodshould be defined to implement the present invention. Walsh codes aregiven as orthogonal sequences by way of example in embodiments of thepresent invention.

1. Mask Sequence Generating Method

The present invention pertains to encoding and decoding of TFCI bits anduse of an extended Reed Muller code in an IMT 2000 system. For thispurpose, predetermined sequences are used and the sequences should havea minimum distance that ensures excellent error correction performance.

A significant parameter that determines the performance or capability ofa linear error correcting code is a minimum distance between codewordsof the error correcting code. The Hamming weight of a codeword is thenumber of its symbols other than 0. If a codeword is given as “0111”,its Hamming weight is 3. The smallest Hamming weight of a codewordexcept all “0” codeword is called a minimum weight and the minimumdistance of each binary linear code is equal to the minimum weight. Alinear error correcting code has a better error correcting performanceas its minimum distance is increased. For details, see “The Theory ofError-Correcting Codes”, F. J. Macwilliams and N. J. A. Sloane,North-Holland (hereinafter, referred to as reference 2).

An extended Reed Muller code can be derived from a set of sequences eachbeing the sum of the elements of an m-sequence and a predeterminedsequence. To use the sequence set as a linear error correcting code, thesequence set should have a large minimum distance. Such sequence setsinclude a Kasami sequence set, a Gold sequence set, and a Kerdocksequence set. If the total length of a sequence in such a sequence setis L=2^(2m), a minimum distance=(2^(2m)−2^(m))/2. For L=2^(2m+1), theminimum distance=(2^(2m+1)−2^(2m))/2. That is, if L=32, the minimumdistance=12.

A description will be made of a method of generating a linear errorcorrecting code with excellent performance, i.e., an extended errorcorrecting code (Walsh codes and mask sequences).

According to a coding theory, there is a column transposition functionfor making Walsh codes from m-sequences in a group which has been formedby cyclically shifting an originating m-sequence by one to ‘n’ times,where the ‘n’ is a length of the m-sequence. In other words, each of them-sequences is formed by cyclically shifting the originating m-sequenceby a particular number of times. The column transposition function is aconverting function which converts the sequences in the m-sequence groupto Walsh codes. We assume there is a sequence such as a Gold sequence ora Kasami sequence which is formed by adding the originating m-sequencewith another originating m-sequence. Another group of m-sequences issimilarly formed by cyclically shifting the other originating m-sequenceone to ‘n’ times, where ‘n’ is the length of the predetermined sequence.Afterwards, a reverse column transposition function is applied to thesecond group of m-sequences formed from the other originatingm-sequence. The application of the reverse column transposition functionto the second group of m-sequences creates another set of sequenceswhich shall be defined as mask sequences.

In an embodiment of the present invention, a mask sequence generatingmethod is described in connection with generation of a (2^(n), n+k) code(extended Reed Muller code) (here, k=1, . . . , n+1) using a Goldsequence set. The (2^(n), n+k) code represents output of a 2^(n)-symbolTFCI codeword for the input of (n+k) TFCI bits (input information bits).It is well known that a Gold sequence can be expressed as the sum of twodifferent m-sequences. To generate the (2^(n), n+k) code, therefore,Gold sequences of length (2^(n)−1) should be produced. Here, a Goldsequence is the sum of two m-sequences m₁(t) and m₂(t) that aregenerated from generator polynomials f1(x) and f2(x). Given thegenerator polynomials f1(x) and f2(x), the m-sequences m₁(t) and m₂(t)are computed using a Trace function.m₁(t) = Tr(A  α^(t))  t = 0, 1, …  , 30  and $\begin{matrix}{{{{Tr}(a)} = {\sum\limits_{k = 0}^{n - 1}a^{2k}}},\quad{a \in {G\quad{F\left( 2^{n} \right)}}}} & \left( {{Eq}.\quad 1} \right)\end{matrix}$where A is determined by the initial value of an m-sequence, α is theroot of the polynomial, and n is the order of the polynomial.

FIG. 7 is a flowchart illustrating a mask sequence generating procedurefor use in generating a (2^(n), n+k) code from a Gold sequence set.

Referring to FIG. 7, m-sequences m₁(t) and m₂(t) are generated in Eq. 1using the generator polynomials f1(x) and f2(x), respectively in step710. In step 712, a sequence transposition function σ(t) is calculatedto make Walsh codes from a sequence set having m-sequences formed bycyclically shifting m₂(t) 0 to n-2 times where all ‘0’ column isinserted in front of the m-sequences made from m₂(t), as shown below:σ:  {0, 1, 2, …  , 2^(n) − 2}− > {1, 2, 3, …  , 2^(n) − 1}$\begin{matrix}{{{\sigma(t)} = {{\sum\limits_{i = 0}^{n - 1}{{m_{2}\left( {t + i} \right)}2^{n - 1 - i}\quad t}} = 0}},1,2,\ldots} & \left( {{Eq}.\quad 2} \right)\end{matrix}$

A set of 31 sequences produced by cyclically shifting the m-sequencem₁(t) 0 to 30 times are column-transposed with the use of σ⁻¹(t)+2derived from the reverse function of σ(t) in step 730. Then, 0s areadded to the start of each of the resulting column-transposed sequencesto make the length of the sequence 2^(n). Thus, a set d_(i)(t) of(2^(n)−1) sequences of length 2^(n) (i=0, . . . , 2^(n)−2, t=1, . . . ,2^(n)) are generated.{d_(i)(t)❘t = 1, …  , 2^(n), i = 0, …  , 2^(n) − 2} $\begin{matrix}{{d_{i}(t)} = \begin{pmatrix}{0,} & {{if},{t = 1}} \\{{m_{1}\left( {{\sigma^{- 1}\left( {t + i} \right)} + 2} \right)},} & {{if},{t = 2},3,\ldots\quad,2^{n}}\end{pmatrix}} & \left( {{Eq}.\quad 3} \right)\end{matrix}$

A plurality of d_(i)(t) are mask functions that can be used as 31 masks.

d_(i)(t) is characterized in that two different masks among the abovemasks are added to one of (2^(n)−1) masks except for the two masks. Tofurther generalize it, each of the (2^(n)−1) masks can be expressed asthe sum of at least two of particular n masks. The n masks are calledbasis mask sequences. When the (2^(n), n+k) code is to be generated, thetotal number of necessary codewords is 2^(n+k) for n+k input informationbits (TFCI bits). The number of 2^(n) orthogonal sequences (Walshsequences) and their complements, i.e. biorthogonal sequences, is2^(n)×2=2^(n+1). 2^(k−1)−1(=(2^(n+k)/2^(n+1))−1) masks that are not 0sare needed for generation of the (2^(n), n+k) code. Here, the 2^(k−1)−1masks can be expressed by the use of k−1 basis mask sequences, as statedbefore.

Now, a description will be given of a method of selecting the k−1 basismask sequences. The m-sequence m₁(t) is cyclically shifted 0 to 2^(n−1)times to generate a set of sequences in step 730 of FIG. 7. Here, anm-sequence obtained by cyclically shifting the m-sequence m₁(t) i timesis expressed as Tr(α^(i)·α^(t)) according to Eq. 1. That is, a set ofsequences are generated by cyclically shifting the m-sequence m₁(t) 0 to30 times with respect to an initial sequence A={1, α, . . . , α^(2n−2).Here, linearly independent k−1 basis elements are found from the Galoiselements 1, α, . . . , α² ^(n) ⁻² and mask sequences corresponding tothe output sequences of a Trace function with the k−1 basis elements asan initial sequence become basis mask sequences. A linear independencecondition is expressed as

-   -   α, . . . , α_(k−1): linearly independent        c ₁α₁ +c ₂α₂ + . . . +c _(k−1)α_(k−1)≠0, ∀c ₁ , c ₂ , . . . , c        _(k−1)   (Eq. 4)

To describe the above generalized mask function generation method indetail, how to generate a (32, 10) code using a Gold sequence set willbe described referring to FIG. 7. It is well known that a Gold sequenceis expressed as the sum of different predetermined m-sequences.Therefore, a Gold sequence of length 31 should be generated first inorder to generate the intended (32, 10) code. The Gold sequence is thesum of two m-sequences generated respectively from polynomials x⁵+x²+1and x⁵+x⁴+x+1. Given a corresponding generator polynomial, each of them-sequences m₁(t) and m₂(t) is computed using a Trace function bym₁(t) = Tr(A  α^(t))  t = 0, 1, …  , 30  and $\begin{matrix}{{{{Tr}(a)} = {\sum\limits_{n = 0}^{n - 1}a^{2n}}},\quad{a \in {G\quad{F\left( 2^{5} \right)}}}} & \left( {{Eq}.\quad 5} \right)\end{matrix}$where A is determined by the initial value of the m-sequence, α is theroot of the polynomial, and n is the order of the polynomial, here 5.

FIG. 7 illustrates the mask function generating procedure to generatethe (32, 10) code.

Referring to FIG. 7, m-sequences m₁(t) and m₂(t) are generated in Eq. 1using the generator polynomials f1(x) and f2(x), respectively in step710. In step 712, the column transposition function σ(t) is calculatedto make a Walsh code of the m-sequence m₂(t) byσ:  {0, 1, 2, …  , 30}− > {1, 2, 3, …  , 31} $\begin{matrix}{{\sigma(t)} = {\sum\limits_{i = 0}^{4}{{m_{2}\left( {t - i} \right)}2^{4 - i}}}} & \left( {{Eq}.\quad 6} \right)\end{matrix}$

Then, a set of 31 sequences produced by cyclically shifting them-sequence m₁(t) 0 to 30 times are column-transposed with the use ofσ⁻¹(t)+2 derived from the reverse function of σ(t) in step 730. Then, 0sare added to the start of each of the resulting sequence-transposedsequences to make the length of the sequence 31. Thus, 31 d_(i)(t) oflength 32 are generated. Here, if i =0, . . . , 31, t=1, . . . , 32. Thesequences set generated in step 730 can be expressed as{d_(i)(t)❘t = 1, …  , 32, i = 0, …  , 30} $\begin{matrix}{{d_{i}(t)} = \begin{pmatrix}{0,} & {{if},{t = 1}} \\{{m_{1}\left( {{\sigma^{- 1}\left( {t + i} \right)} + 2} \right)},} & {{if},{t = 2},3,\ldots\quad,32}\end{pmatrix}} & \left( {{Eq}.\quad 7} \right)\end{matrix}$

A plurality of d_(i)(t) obtained from Eq. 7 can be used as 31 masksequences.

d_(i)(t) is characterized in that two different masks among the abovemasks are added to one of the 31 masks except for the two masks. Inother words, each of the 31 masks can be expressed as a sum of 5particular masks. These 5 masks are basis mask sequences.

When the (32, 10) code is to be generated, the total number of necessarycodewords is 2^(n)=1024 for all possible 10 input information bits (TFCIbits). The number of biorthogonal sequences of length 32 is 32×2=64. 15masks are needed to generate the (32, 10) code. The 15 masks can beexpressed as combinations of 4 basis mask sequences.

Now, a description will be given of a method of selecting the 4 basismask sequences. An m-sequence obtained by cyclically shifting them-sequence m₁(t) i times is expressed as Tr(α^(i)·α^(i)) according toEq. 1. That is, a set of sequences are generated by cyclically shiftingthe m-sequence m₁(t) 0 to 30 times with respect to an initial sequenceA={1, α, . . . , α^(2n−2)}. Here, 4 linearly independent basis elementsare found from the Galois elements 1, α, . . . , α^(2n−2) and masksequences corresponding to the output sequences of a Trace function withthe 4 basis elements as an initial sequence becoming basis masksequences. A linear independence condition, is expressed as

-   -   α, β, γ, δ: linearly independent        c ₁ α+c ₂ β+c ₃ γ, +c ₄δ≠0, ∀c ₁ , c ₂ , c ₃ , c ₄   (Eq. 8)

In fact, 1, α, α², α³ in the Galois GF(2⁵) are polynomial sub-bases thatare well known as four linearly independent elements. By replacing thevariable A in Eq. 1 with the polynomial bases, four basis mask sequencesM1, M2, M4, and M8 are achieved.

-   -   M1=00101000011000111111000001110111    -   M2=00000001110011010110110111000111    -   M4=00001010111110010001101100101011    -   M8=00011100001101110010111101010001

There will herein below be given a description of an apparatus andmethod for encoding/decoding a TFCI using basis mask sequences asobtained in the above manner in an IMT 2000 system according toembodiments of the present invention.

2. First Embodiment of Encoding/Decoding Apparatus and Method

FIGS. 8 and 9 are block diagrams of TFCI encoding and decodingapparatuses in an IMT 2000 system according to an embodiment of thepresent invention.

Referring to FIG. 8, 10 TFCI bits a0 to a9 are applied to correspondingmultipliers 840 to 849. A one-bit generator 800 continuously generates apredetermined code bit. That is, since the present invention deals withbiorthogonal sequences, necessary bits are generated to make abiorthogonal sequence out of an orthogonal sequence. For example, theone-bit generator 800 generates bits having is to inverse an orthogonalsequence (i.e., a Walsh code) generated from a basis Walsh codegenerator 810 and thus generate a biorthogonal sequence. The basis Walshcode generator 810 generates basis Walsh codes of a predeterminedlength. The basis Walsh codes refer to Walsh codes from which allintended Walsh codes can be produced through arbitrary addition. Forexample, when Walsh codes of length 32 are used, the basis Walsh codesare 1^(st), 2^(nd), 4^(th), 8^(th), and 16^(th) Walsh codes W1, W2, W4,W8, and W16, wherein:

-   -   W1:01010101010101010101010101010101    -   W2:00110011001100110011001100110011    -   W4:00001111000011110000111100001111    -   W8:00000000111111110000000011111111    -   W16 00000000000000001111111111111111.

A basis mask sequence generator 820 generates a basis mask sequence of apredetermined length. A basis mask sequence generating method hasalready been described before and its details will not be described. Ifa mask sequence of length 32 is used, basis mask sequences are 1^(st),2^(nd), 4^(th), and 8^(th) mask sequences M1, M2, M4, M8, wherein:

-   -   M1:00101000011000111111000001110111    -   M2:00000001110011010110110111000111    -   M4:00001010111110010001101100101011    -   M8:00011100001101110010111101010001.

The multiplier 840 multiplies 1s output from the one-bit generator 800by the input information bit a0 on a symbol basis.

The multiplier 841 multiplies the basis Walsh code W1 received from thebasis Walsh code generator 810 by the input information bit al. Themultiplier 842 multiplies the basis Walsh code W2 received from thebasis Walsh code generator 810 by the input information bit a2. Themultiplier 843 multiplies the basis Walsh code W4 received from thebasis Walsh code generator 810 by the input information bit a3. Themultiplier 844 multiplies the basis Walsh code W8 received from thebasis Walsh code generator 810 by the input information bit a4. Themultiplier 845 multiplies the basis Walsh code W16 received from thebasis Walsh code generator 810 by the input information bit a5. Themultipliers 841 to 845 multiply the received basis Walsh codes W1, W2,W4, W8, and W16 by their corresponding input information bits symbol bysymbol.

Meanwhile, the multiplier 846 multiplies the basis mask sequence M1 bythe input information bit a6. The multiplier 847 multiplies the basismask sequence M2 by the input information bit a7. The multiplier 848multiplies the basis mask sequence M4 by the input information bit a8.The multiplier 849 multiplies the basis mask sequence M8 by the inputinformation bit a9. The multipliers 846 to 849 multiply the receivedbasis mask sequences M1, M2, M4, and M8 by their corresponding inputinformation bits symbol by symbol.

An adder 860 adds the encoded input information bits received from themultipliers 840 to 849 and outputs final code symbols of length 32 bits(a TFCI codeword). The length of the final code symbols (TFCI codeword)is determined by the lengths of the basis Walsh codes generated from thebasis Walsh code generator 810 and the basis mask sequences generatedfrom the basis mask sequence generator 820.

For example, if the input information bits a0 to a9 are “0111011000”,the multiplier 840 multiplies 0 as a0 by is received from the one-bitgenerator 800 and generates 32 code symbols being all “0s”. Themultiplier 841 multiplies 1 as a1 by W1 received from the basis Walshcode generator 810 and generates code symbols“01010101010101010101010101010101”. The multiplier 842 multiplies 1 asa2 by W2 received from the basis Walsh code generator 810 and generatescode symbols “00110011001100110011001100110011”. The multiplier 843multiplies 1 as a3 by W4 received from the basis Walsh code generator810 and generates code symbols “00001111000011110000111100001111”. Themultiplier 844 multiplies 0 as a4 by W8 received from the basis Walshcode generator 810 and generates 32 code symbols being all “0s”. Themultiplier 845 multiplies 1 as a5 by W16 received from the basis Walshcode generator 810 and generates “00000000000000001111111111111111”. Themultiplier 846 multiplies 1 as a6 by M1 received from the basis masksequence generator 820 and generates “00101000011000111111000001110111”.The multiplier 847 multiplies 0 as a7 by M2 received from the basis masksequence generator 820 and generates 32 code symbols being all 0s. Themultiplier 848 multiplies 0 as a8 by M4 received from the basis masksequence generator 820 and generates 32 code symbols being all 0s. Themultiplier 849 multiplies 0 as a9 by M8 received from the basis masksequence generator 820 and generates 32 code symbols being all 0s. Theadder 860 adds the code symbols received from the multipliers 840 to 849and outputs final code symbols “01000001000010100110011011100001”. Thefinal code symbols can be achieved by adding the basis Walsh codes W1,W2, W4 and W16 corresponding to the information bits 1s to the basismask sequence M1 symbol by symbol. In other words, the basis Walsh codesW1, W2, W4 and W16 are summed to W23 and the Walsh code W23 and thebasis mask sequence M1 are added to form the TFCI codeword (final codesymbols) (=W23+M1) which is outputted from the adder 860.

FIG. 11 is a flowchart illustrating an embodiment of a TFCI encodingprocedure in an IMT 2000 system according to the present invention.

Referring to FIG. 11, 10 input information bits (i.e., TFCI bits) arereceived and variables sum and j are set to an initial value 0 in step1100. The variable sum indicates final code symbols, and j indicates thecount number of final code symbols output after symbol-basis addition.In step 1110, it is determined whether j is 32 in view of the length 32symbols of Walsh codes and mask sequences used for encoding the inputinformation bits. Step 1110 is performed in order to check whether theinput information bits are all encoded with the Walsh codes and the masksequences symbol by symbol.

If j is not 32 in step 1110, which implies that the input informationbits are not encoded completely with respect to all symbols of the Walshcodes, the mask sequences, j^(th) symbols W1(j), W2(j), W4(j), W8(j),and W16(j) of the basis Walsh codes W1, W2, W4, W8, and W16 and j^(th)symbols M1(j), M2(j), M4(j), and M8(j) of the basis mask sequences M1,M2, M4, and M8 are received in step 1120. Then, the received symbols aremultiplied by the input information bits on a symbol basis and thesymbol products are summed in step 1130. The sum becomes the variablesum.

Step 1130 can be expressed assum=a 0+a 1·W1(j)+a 2·W2(j)+a 3·W4(j)+a 4·W8(j)+a 5·W16(j)+a 6·M1(j)+a7·M2(j)+a 8·M4(j)+a 9·M8(j)   (Eq. 9)

As noted from Eq. 9, the input information bits are multiplied bycorresponding symbols of the basis Walsh codes and basis mask sequences,symbol products are summed, and the sum becomes an intended code symbol.

In step 1140, sum indicating the achieved j^(th) code symbol, is output.j is increased by 1 in step 1150 and then the procedure returns to step1110. Meanwhile, if j is 32 in step 1110, the encoding procedure ends.

The encoding apparatus of FIG. 8 according to the embodiment of thepresent invention can support extended TFCIs as well as basic TFCIs.Encoders for supporting an extended TFCI include a (32, 10) encoder, a(32, 9) encoder, and a (32, 7) encoder.

For the input of 10 input information bits, the (32, 10) encoder outputsa combination of 32 Walsh codes of length 32, 32 bi-orthogonal codesinverted from the Walsh codes, and 15 mask sequences. The 32 Walsh codescan be generated from combinations of 5 basis Walsh codes. The 32bi-orthogonal codes can be obtained by adding 1 to the 32 symbols ofeach Walsh code. This results has the same effect as multiplication of−1 by the 32 Walsh codes viewed as real numbers. The 15 mask sequencescan be achieved through combinations of 5 basis mask sequences.Therefore, a total of 1024 codewords can be produced from the (32, 10)encoder.

The (32, 9) encoder receives 9 input information bits and outputs acombination of 32 Walsh codes of length 32, 32 bi-orthogonal codesinverted from the Walsh codes, and 4 mask sequences. The 4 masksequences are obtained by combing two of 4 basis mask sequences.

The (32, 7) encoder receives 7 input information bits and outputs acombination of 32 Walsh codes of length among the 1024 codewords, 32bi-orthogonal codes inverted from the Walsh codes, and one of 4 basismask sequences.

The above encoders for providing extended TFCIs have a minimum distance12 and can be implemented by blocking input and output of at least ofthe 4 basis mask sequences generated from the basis mask sequences 820.

That is, the (32, 9) encoder can be implemented by blocking input andoutput of one of the four basis mask sequences generated from the basismask sequence generator 820 shown in FIG. 8. The (32, 8) encoder can beimplemented by blocking input and output of two of the basis masksequences generated from the basis mask sequence generator 820. The (32,7) encoder can be implemented by blocking input and output of three ofthe basis mask sequences generated from the basis mask sequencegenerator 820. As described above, the encoding apparatus according tothe embodiment of the present invention can encode flexibly according tothe number of input information bits, that is, the number of TFCI bitsto be transmitted and maximizes a minimum distance that determined theperformance of the encoding apparatus.

Codewords in the above encoding apparatus are sequences obtained bycombining 32 Walsh codes of length 32, 32 bi-orthogonal codes resultingfrom adding 1s to the Walsh codes, and 15 mask sequences of length 15.The structure of the codewords is shown in FIG. 13.

For better understanding of the TFC bits encoding procedure, Tables 1ato 1f list code symbols (TFCI codewords) versus 10 TFCI bits. TABLE 1a0000000000: 00000000000000000000000000000000 0000000001:11111111111111111111111111111111 0000000010:01010101010101010101010101010101 0000000011:10101010101010101010101010101010 0000000100:00110011001100110011001100110011 0000000101:11001100110011001100110011001100 0000000110:01100110011001100110011001100110 0000000111:10011001100110011001100110011001 0000001000:00001111000011110000111100001111 0000001001:11110000111100001111000011110000 0000001010:01011010010110100101101001011010 0000001011:10100101101001011010010110100101 0000001100:00111100001111000011110000111100 0000001101:11000011110000111100001111000011 0000001110:01101001011010010110100101101001 0000001111:10010110100101101001011010010110 0000010000:00000000111111110000000011111111 0000010001:11111111000000001111111100000000 0000010010:01010101101010100101010110101010 0000010011:10101010010101011010101001010101 0000010100:00110011110011000011001111001100 0000010101:11001100001100111100110000110011 0000010110:01100110100110010110011010011001 0000010111:10011001011001101001100101100110 0000011000:00001111111100000000111111110000 0000011001:11110000000011111111000000001111 0000011010:01011010101001010101101010100101 0000011011:10100101010110101010010101011010 0000011100:00111100110000110011110011000011 0000011101:11000011001111001100001100111100 0000011110:01101001100101100110100110010110 0000011111:10010110011010011001011001101001 0000100000:00000000000000001111111111111111 0000100001:11111111111111110000000000000000 0000100010:01010101010101011010101010101010 0000100011:10101010101010100101010101010101 0000100100:00110011001100111100110011001100 0000100101:11001100110011000011001100110011 0000100110:01100110011001101001100110011001 0000100111:10011001100110010110011001100110 0000101000:00001111000011111111000011110000 0000101001:11110000111100000000111100001111 0000101010:01011010010110101010010110100101 0000101011:10100101101001010101101001011010 0000101100:00111100001111001100001111000011 0000101101:11000011110000110011110000111100 0000101110:01101001011010011001011010010110 0000101111:10010110100101100110100101101001 0000110000:00000000111111111111111100000000 0000110001:11111111000000000000000011111111 0000110010:01010101101010101010101001010101 0000110011:10101010010101010101010110101010 0000110100:00110011110011001100110000110011 0000110101:11001100001100110011001111001100 0000110110:01100110100110011001100101100110 0000110111:10011001011001100110011010011001 0000111000:00001111111100001111000000001111 0000111001:11110000000011110000111111110000 0000111010:01011010101001011010010101011010 0000111011:10100101010110100101101010100101 0000111100:00111100110000111100001100111100 0000111101:11000011001111000011110011000011 0000111110:01101001100101101001011001101001 0000111111:10010110011010010110100110010110 0001000000:00101000011000111111000001110111 0001000001:11010111100111000000111110001000 0001000010:01111101001101101010010100100010 0001000011:10000010110010010101101011011101 0001000100:00011011010100001100001101000100 0001000101:11100100101011110011110010111011 0001000110:01001110000001011001011000010001 0001000111:10110001111110100110100111101110 0001001000:00100111011011001111111101111000 0001001001:11011000100100110000000010000111 0001001010:01110010001110011010101000101101 0001001011:10001101110001100101010111010010 0001001100:00010100010111111100110001001011 0001001101:11101011101000000011001110110100 0001001110:01000001000010101001100100011110 0001001111:10111110111101010110011011100001 0001010000:00101000100111001111000010001000 0001010001:11010111011000110000111101110111 0001010010:01111101110010011010010111011101 0001010011:10000010001101100101101000100010 0001010100:00011011101011111100001110111011 0001010101:11100100010100000011110001000100 0001010110:01001110111110101001011011101110 0001010111:10110001000001010110100100010001 0001011000:00100111100100111111111110000111 0001011001:11011000011011000000000001111000 0001011010:01110010110001101010101011010010 0001011011:10001101001110010101010100101101 0001011100:00010100101000001100110010110100 0001011101:11101011010111110011001101001011 0001011110:01000001111101011001100111100001 0001011111:10111110000010100110011000011110 0001100000:00101000011000110000111110001000 0001100001:11010111100111001111000001110111 0001100010:01111101001101100101101011011101 0001100011:10000010110010011010010100100010 0001100100:00011011010100000011110010111011 0001100101:11100100101011111100001101000100 0001100110:01001110000001010110100111101110 0001100111:10110001111110101001011000010001 0001101000:00100111011011000000000010000111 0001101001:11011000100100111111111101111000 0001101010:01110010001110010101010111010010 0001101011:10001101110001101010101000101101 0001101100:00010100010111110011001110110100 0001101101:11101011101000001100110001001011 0001101110:01000001000010100110011011100001 0001101111:10111110111101011001100100011110 0001110000:00101000100111000000111101110111 0001110001:11010111011000111111000010001000 0001110010:01111101110010010101101000100010 0001110011:10000010001101101010010111011101 0001110100:00011011101011110011110001000100 0001110101:11100100010100001100001110111011 0001110110:01001110111110100110100100010001 0001110111:10110001000001011001011011101110 0001111000:00100111100100110000000001111000 0001111001:11011000011011001111111110000111 0001111010:01110010110001100101010100101101 0001111011:10001101001110011010101011010010 0001111100:00010100101000000011001101001011 0001111101:11101011010111111100110010110100 0001111110:01000001111101010110011000011110 0001111111:10111110000010101001100111100001 0010000000:00000001110011010110110111000111 0010000001:11111110001100101001001000111000 0010000010:01010100100110000011100010010010 0010000011:10101011011001111100011101101101 0010000100:00110010111111100101111011110100 0010000101:11001101000000011010000100001011 0010000110:01100111101010110000101110100001 0010000111:10011000010101001111010001011110 0010001000:00001110110000100110001011001000 0010001001:11110001001111011001110100110111 0010001010:01011011100101110011011110011101 0010001011:10100100011010001100100001100010 0010001100:00111101111100010101000111111011 0010001101:11000010000011101010111000000100 0010001110:01101000101001000000010010101110 0010001111:10010111010110111111101101010001 0010010000:00000001001100100110110100111000 0010010001:11111110110011011001001011000111 0010010010:01010100011001110011100001101101 0010010011:10101011100110001100011110010010 0010010100:00110010000000010101111000001011 0010010101:11001101111111101010000111110100 0010010110:01100111010101000000101101011110 0010010111:10011000101010111111010010100001 0010011000:00001110001111010110001000110111 0010011001:11110001110000101001110111001000 0010011010:01011011011010000011011101100010 0010011011:10100100100101111100100010011101 0010011100:00111101000011100101000100000100 0010011101:11000010111100011010111011111011 0010011110:01101000010110110000010001010001 0010011111:10010111101001001111101110101110 0010100000:00000001110011011001001000111000 0010100001:11111110001100100110110111000111 0010100010:01010100100110001100011101101101 0010100011:10101011011001110011100010010010 0010100100:00110010111111101010000100001011 0010100101:11001101000000010101111011110100 0010100110:01100111101010111111010001011110 0010100111:10011000010101000000101110100001 0010101000:00001110110000101001110100110111 0010101001:11110001001111010110001011001000 0010101010:01011011100101111100100001100010 0010101011:10100100011010000011011110011101 0010101100:00111101111100011010111000000100 0010101101:11000010000011100101000111111011 0010101110:01101000101001001111101101010001 0010101111:10010111010110110000010010101110 0010110000:00000001001100101001001011000111 0010110001:11111110110011010110110100111000 0010110010:01010100011001111100011110010010 0010110011:10101011100110000011100001101101 0010110100:00110010000000011010000111110100 0010110101:11001101111111100101111000001011 0010110110:01100111010101001111010010100001 0010110111:10011000101010110000101101011110 0010111000:00001110001111011001110111001000 0010111001:11110001110000100110001000110111 0010111010:01011011011010001100100010011101 0010111011:10100100100101110011011101100010 0010111100:00111101000011101010111011111011 0010111101:11000010111100010101000100000100 0010111110:01101000010110111111101110101110 0010111111:10010111101001000000010001010001 0011000000:00101001101011101001110110110000 0011000001:11010110010100010110001001001111 0011000010:01111100111110111100100011100101 0011000011:10000011000001000011011100011010 0011000100:00011010100111011010111010000011 0011000101:11100101011000100101000101111100 0011000110:01001111110010001111101111010110 0011000111:10110000001101110000010000101001 0011001000:00100110101000011001001010111111

TABLE 1b 0011001001: 11011001010111100110110101000000 0011001010:01110011111101001100011111101010 0011001011:10001100000010110011100000010101 0011001100:00010101100100101010000110001100 0011001101:11101010011011010101111001110011 0011001110:01000000110001111111010011011001 0011001111:10111111001110000000101100100110 0011010000:00101001010100011001110101001111 0011010001:11010110101011100110001010110000 0011010010:01111100000001001100100000011010 0011010011:10000011111110110011011111100101 0011010100:00011010011000101010111001111100 0011010101:11100101100111010101000110000011 0011010110:01001111001101111111101100101001 0011010111:10110000110010000000010011010110 0011011000:00100110010111101001001001000000 0011011001:11011001101000010110110110111111 0011011010:01110011000010111100011100010101 0011011011:10001100111101000011100011101010 0011011100:00010101011011011010000101110011 0011011101:11101010100100100101111010001100 0011011110:01000000001110001111010000100110 0011011111:10111111110001110000101111011001 0011100000:00101001101011100110001001001111 0011100001:11010110010100011001110110110000 0011100010:01111100111110110011011100011010 0011100011:10000011000001001100100011100101 0011100100:00011010100111010101000101111100 0011100101:11100101011000101010111010000011 0011100110:01001111110010000000010000101001 0011100111:10110000001101111111101111010110 0011101000:00100110101000010110110101000000 0011101001:11011001010111101001001010111111 0011101010:01110011111101000011100000010101 0011101011:10001100000010111100011111101010 0011101100:00010101100100100101111001110011 0011101101:11101010011011011010000110001100 0011101110:01000000110001110000101100100110 0011101111:10111111001110001111010011011001 0011110000:00101001010100010110001010110000 0011110001:11010110101011101001110101001111 0011110010:01111100000001000011011111100101 0011110011:10000011111110111100100000011010 0011110100:00011010011000100101000110000011 0011110101:11100101100111011010111001111100 0011110110:01001111001101110000010011010110 0011110111:10110000110010001111101100101001 0011111000:00100110010111100110110110111111 0011111001:11011001101000011001001001000000 0011111010:01110011000010110011100011101010 0011111011:10001100111101001100011100010101 0011111100:00010101011011010101111010001100 0011111101:11101010100100101010000101110011 0011111110:01000000001110000000101111011001 0011111111:10111111110001111111010000100110 0100000000:00001010111110010001101100101011 0100000001:11110101000001101110010011010100 0100000010:01011111101011000100111001111110 0100000011:10100000010100111011000110000001 0100000100:00111001110010100010100000011000 0100000101:11000110001101011101011111100111 0100000110:01101100100111110111110101001101 0100000111:10010011011000001000001010110010 0100001000:00000101111101100001010000100100 0100001001:11111010000010011110101111011011 0100001010:01010000101000110100000101110001 0100001011:10101111010111001011111010001110 0100001100:00110110110001010010011100010111 0100001101:11001001001110101101100011101000 0100001110:01100011100100000111001001000010 0100001111:10011100011011111000110110111101 0100010000:00001010000001100001101111010100 0100010001:11110101111110011110010000101011 0100010010:01011111010100110100111010000001 0100010011:10100000101011001011000101111110 0100010100:00111001001101010010100011100111 0100010101:11000110110010101101011100011000 0100010110:01101100011000000111110110110010 0100010111:10010011100111111000001001001101 0100011000:00000101000010010001010011011011 0100011001:11111010111101101110101100100100 0100011010:01010000010111000100000110001110 0100011011:10101111101000111011111001110001 0100011100:00110110001110100010011111101000 0100011101:11001001110001011101100000010111 0100011110:01100011011011110111001010111101 0100011111:10011100100100001000110101000010 0100100000:00001010111110011110010011010100 0100100001:11110101000001100001101100101011 0100100010:01011111101011001011000110000001 0100100011:10100000010100110100111001111110 0100100100:00111001110010101101011111100111 0100100101:11000110001101010010100000011000 0100100110:01101100100111111000001010110010 0100100111:10010011011000000111110101001101 0100101000:00000101111101101110101111011011 0100101001:11111010000010010001010000100100 0100101010:01010000101000111011111010001110 0100101011:10101111010111000100000101110001 0100101100:00110110110001011101100011101000 0100101101:11001001001110100010011100010111 0100101110:01100011100100001000110110111101 0100101111:10011100011011110111001001000010 0100110000:00001010000001101110010000101011 0100110001:11110101111110010001101111010100 0100110010:01011111010100111011000101111110 0100110011:10100000101011000100111010000001 0100110100:00111001001101011101011100011000 0100110101:11000110110010100010100011100111 0100110110:01101100011000001000001001001101 0100110111:10010011100111110111110110110010 0100111000:00000101000010011110101100100100 0100111001:11111010111101100001010011011011 0100111010:01010000010111001011111001110001 0100111011:10101111101000110100000110001110 0100111100:00110110001110101101100000010111 0100111101:11001001110001010010011111101000 0100111110:01100011011011111000110101000010 0100111111:10011100100100000111001010111101 0101000000:00100010100110101110101101011100 0101000001:11011101011001010001010010100011 0101000010:01110111110011111011111000001001 0101000011:10001000001100000100000111110110 0101000100:00010001101010011101100001101111 0101000101:11101110010101100010011110010000 0101000110:01000100111111001000110100111010 0101000111:10111011000000110111001011000101 0101001000:00101101100101011110010001010011 0101001001:11010010011010100001101110101100 0101001010:01111000110000001011000100000110 0101001011:10000111001111110100111011111001 0101001100:00011110101001101101011101100000 0101001101:11100001010110010010100010011111 0101001110:01001011111100111000001000110101 0101001111:10110100000011000111110111001010 0101010000:00100010011001011110101110100011 0101010001:11011101100110100001010001011100 0101010010:01110111001100001011111011110110 0101010011:10001000110011110100000100001001 0101010100:00010001010101101101100010010000 0101010101:11101110101010010010011101101111 0101010110:01000100000000111000110111000101 0101010111:10111011111111000111001000111010 0101011000:00101101011010101110010010101100 0101011001:11010010100101010001101101010011 0101011010:01111000001111111011000111111001 0101011011:10000111110000000100111000000110 0101011100:00011110010110011101011110011111 0101011101:11100001101001100010100001100000 0101011110:01001011000011001000001011001010 0101011111:10110100111100110111110100110101 0101100000:00100010100110100001010010100011 0101100001:11011101011001011110101101011100 0101100010:01110111110011110100000111110110 0101100011:10001000001100001011111000001001 0101100100:00010001101010010010011110010000 0101100101:11101110010101101101100001101111 0101100110:01000100111111000111001011000101 0101100111:10111011000000111000110100111010 0101101000:00101101100101010001101110101100 0101101001:11010010011010101110010001010011 0101101010:01111000110000000100111011111001 0101101011:10000111001111111011000100000110 0101101100:00011110101001100010100010011111 0101101101:11100001010110011101011101100000 0101101110:01001011111100110111110111001010 0101101111:10110100000011001000001000110101 0101110000:00100010011001010001010001011100 0101110001:11011101100110101110101110100011 0101110010:01110111001100000100000100001001 0101110011:10001000110011111011111011110110 0101110100:00010001010101100010011101101111 0101110101:11101110101010011101100010010000 0101110110:01000100000000110111001000111010 0101110111:10111011111111001000110111000101 0101111000:00101101011010100001101101010011 0101111001:11010010100101011110010010101100 0101111010:01111000001111110100111000000110 0101111011:10000111110000001011000111111001 0101111100:00011110010110010010100001100000 0101111101:11100001101001101101011110011111 0101111110:01001011000011000111110100110101 0101111111:10110100111100111000001011001010 0110000000:00001011001101000111011011101100 0110000001:11110100110010111000100100010011 0110000010:01011110011000010010001110111001 0110000011:10100001100111101101110001000110 0110000100:00111000000001110100010111011111 0110000101:11000111111110001011101000100000 0110000110:01101101010100100001000010001010 0110000111:10010010101011011110111101110101 0110001000:00000100001110110111100111100011 0110001001:11111011110001001000011000011100 0110001010:01010001011011100010110010110110 0110001011:10101110100100011101001101001001 0110001100:00110111000010000100101011010000 0110001101:11001000111101111011010100101111 0110001110:01100010010111010001111110000101 0110001111:10011101101000101110000001111010 0110010000:00001011110010110111011000010011 0110010001:11110100001101001000100111101100

TABLE 1c 0110010010: 01011110100111100010001101000110 0110010011:10100001011000011101110010111001 0110010100:00111000111110000100010100100000 0110010101:11000111000001111011101011011111 0110010110:01101101101011010001000001110101 0110010111:10010010010100101110111110001010 0110011000:00000100110001000111100100011100 0110011001:11111011001110111000011011100011 0110011010:01010001100100010010110001001001 0110011011:10101110011011101101001110110110 0110011100:00110111111101110100101000101111 0110011101:11001000000010001011010111010000 0110011110:01100010101000100001111101111010 0110011111:10011101010111011110000010000101 0110100000:00001011001101001000100100010011 0110100001:11110100110010110111011011101100 0110100010:01011110011000011101110001000110 0110100011:10100001100111100010001110111001 0110100100:00111000000001111011101000100000 0110100101:11000111111110000100010111011111 0110100110:01101101010100101110111101110101 0110100111:10010010101011010001000010001010 0110101000:00000100001110111000011000011100 0110101001:11111011110001000111100111100011 0110101010:01010001011011101101001101001001 0110101011:10101110100100010010110010110110 0110101100:00110111000010001011010100101111 0110101101:11001000111101110100101011010000 0110101110:01100010010111011110000001111010 0110101111:10011101101000100001111110000101 0110110000:00001011110010111000100111101100 0110110001:11110100001101000111011000010011 0110110010:01011110100111101101110010111001 0110110011:10100001011000010010001101000110 0110110100:00111000111110001011101011011111 0110110101:11000111000001110100010100100000 0110110110:01101101101011011110111110001010 0110110111:10010010010100100001000001110101 0110111000:00000100110001001000011011100011 0110111001:11111011001110110111100100011100 0110111010:01010001100100011101001110110110 0110111011:10101110011011100010110001001001 0110111100:00110111111101111011010111010000 0110111101:11001000000010000100101000101111 0110111110:01100010101000101110000010000101 0110111111:10011101010111010001111101111010 0111000000:00100011010101111000011010011011 0111000001:11011100101010000111100101100100 0111000010:01110110000000101101001111001110 0111000011:10001001111111010010110000110001 0111000100:00010000011001001011010110101000 0111000101:11101111100110110100101001010111 0111000110:01000101001100011110000011111101 0111000111:10111010110011100001111100000010 0111001000:00101100010110001000100110010100 0111001001:11010011101001110111011001101011 0111001010:01111001000011011101110011000001 0111001011:10000110111100100010001100111110 0111001100:00011111011010111011101010100111 0111001101:11100000100101000100010101011000 0111001110:01001010001111101110111111110010 0111001111:10110101110000010001000000001101 0111010000:00100011101010001000011001100100 0111010001:11011100010101110111100110011011 0111010010:01110110111111011101001100110001 0111010011:10001001000000100010110011001110 0111010100:00010000100110111011010101010111 0111010101:11101111011001000100101010101000 0111010110:01000101110011101110000000000010 0111010111:10111010001100010001111111111101 0111011000:00101100101001111000100101101011 0111011001:11010011010110000111011010010100 0111011010:01111001111100101101110000111110 0111011011:10000110000011010010001111000001 0111011100:00011111100101001011101001011000 0111011101:11100000011010110100010110100111 0111011110:01001010110000011110111100001101 0111011111:10110101001111100001000011110010 0111100000:00100011010101110111100101100100 0111100001:11011100101010001000011010011011 0111100010:01110110000000100010110000110001 0111100011:10001001111111011101001111001110 0111100100:00010000011001000100101001010111 0111100101:11101111100110111011010110101000 0111100110:01000101001100010001111100000010 0111100111:10111010110011101110000011111101 0111101000:00101100010110000111011001101011 0111101001:11010011101001111000100110010100 0111101010:01111001000011010010001100111110 0111101011:10000110111100101101110011000001 0111101100:00011111011010110100010101011000 0111101101:11100000100101001011101010100111 0111101110:01001010001111100001000000001101 0111101111:10110101110000011110111111110010 0111110000:00100011101010000111100110011011 0111110001:11011100010101111000011001100100 0111110010:01110110111111010010110011001110 0111110011:10001001000000101101001100110001 0111110100:00010000100110110100101010101000 0111110101:11101111011001001011010101010111 0111110110:01000101110011100001111111111101 0111110111:10111010001100011110000000000010 0111111000:00101100101001110111011010010100 0111111001:11010011010110001000100101101011 0111111010:01111001111100100010001111000001 0111111011:10000110000011011101110000111110 0111111100:00011111100101000100010110100111 0111111101:11100000011010111011101001011000 0111111110:01001010110000010001000011110010 0111111111:10110101001111101110111100001101 1000000000:00011100001101110010111101010001 1000000001:11100011110010001101000010101110 1000000010:01001001011000100111101000000100 1000000011:10110110100111011000010111111011 1000000100:00101111000001000001110001100010 1000000101:11010000111110111110001110011101 1000000110:01111010010100010100100100110111 1000000111:10000101101011101011011011001000 1000001000:00010011001110000010000001011110 1000001001:11101100110001111101111110100001 1000001010:01000110011011010111010100001011 1000001011:10111001100100101000101011110100 1000001100:00100000000010110001001101101101 1000001101:11011111111101001110110010010010 1000001110:01110101010111100100011000111000 1000001111:10001010101000011011100111000111 1000010000:00011100110010000010111110101110 1000010001:11100011001101111101000001010001 1000010010:01001001100111010111101011111011 1000010011:10110110011000101000010100000100 1000010100:00101111111110110001110010011101 1000010101:11010000000001001110001101100010 1000010110:01111010101011100100100111001000 1000010111:10000101010100011011011000110111 1000011000:00010011110001110010000010100001 1000011001:11101100001110001101111101011110 1000011010:01000110100100100111010111110100 1000011011:10111001011011011000101000001011 1000011100:00100000111101000001001110010010 1000011101:11011111000010111110110001101101 1000011110:01110101101000010100011011000111 1000011111:10001010010111101011100100111000 1000100000:00011100001101111101000010101110 1000100001:11100011110010000010111101010001 1000100010:01001001011000101000010111111011 1000100011:10110110100111010111101000000100 1000100100:00101111000001001110001110011101 1000100101:11010000111110110001110001100010 1000100110:01111010010100011011011011001000 1000100111:10000101101011100100100100110111 1000101000:00010011001110001101111110100001 1000101001:11101100110001110010000001011110 1000101010:01000110011011011000101011110100 1000101011:10111001100100100111010100001011 1000101100:00100000000010111110110010010010 1000101101:11011111111101000001001101101101 1000101110:01110101010111101011100111000111 1000101111:10001010101000010100011000111000 1000110000:00011100110010001101000001010001 1000110001:11100011001101110010111110101110 1000110010:01001001100111011000010100000100 1000110011:10110110011000100111101011111011 1000110100:00101111111110111110001101100010 1000110101:11010000000001000001110010011101 1000110110:01111010101011101011011000110111 1000110111:10000101010100010100100111001000 1000111000:00010011110001111101111101011110 1000111001:11101100001110000010000010100001 1000111010:01000110100100101000101000001011 1000111011:10111001011011010111010111110100 1000111100:00100000111101001110110001101101 1000111101:11011111000010110001001110010010 1000111110:01110101101000011011100100111000 1000111111:10001010010111100100011011000111 1001000000:00110100010101001101111100100110 1001000001:11001011101010110010000011011001 1001000010:01100001000000011000101001110011 1001000011:10011110111111100111010110001100 1001000100:00000111011001111110110000010101 1001000101:11111000100110000001001111101010 1001000110:01010010001100101011100101000000 1001000111:10101101110011010100011010111111 1001001000:00111011010110111101000000101001 1001001001:11000100101001000010111111010110 1001001010:01101110000011101000010101111100 1001001011:10010001111100010111101010000011 1001001100:00001000011010001110001100011010 1001001101:11110111100101110001110011100101 1001001110:01011101001111011011011001001111 1001001111:10100010110000100100100110110000 1001010000:00110100101010111101111111011001 1001010001:11001011010101000010000000100110 1001010010:01100001111111101000101010001100 1001010011:10011110000000010111010101110011 1001010100:00000111100110001110110011101010 1001010101:11111000011001110001001100010101 1001010110:01010010110011011011100110111111 1001010111:10101101001100100100011001000000 1001011000:00111011101001001101000011010110 1001011001:11000100010110110010111100101001 1001011010:01101110111100011000010110000011

TABLE 1d 1001011011: 10010001000011100111101001111100 1001011100:00001000100101111110001111100101 1001011101:11110111011010000001110000011010 1001011110:01011101110000101011011010110000 1001011111:10100010001111010100100101001111 1001100000:0110100010101000010000011011001 1001100001:11001011101010111101111100100110 1001100010:1100001000000010111010110001100 1001100011:10011110111111101000101001110011 1001100100:00000111011001110001001111101010 1001100101:1111000100110001110110000010101 1001100110:01010010001100100100011010111111 1001100111:10101101110011011011100101000000 1001101000:00111011010110110010111111010110 1001101001:1000100101001001101000000101001 1001101010:01101110000011100111101010000011 1001101011:10010001111100011000010101111100 1001101100:0001000011010000001110011100101 1001101101:11110111100101111110001100011010 1001101110:01011101001111010100100110110000 1001101111:10100010110000101011011001001111 1001110000:0110100101010110010000000100110 1001110001:11001011010101001101111111011001 1001110010:01100001111111100111010101110011 1001110011:10011110000000011000101010001100 1001110100:0000111100110000001001100010101 1001110101:11111000011001111110110011101010 1001110110:1010010110011010100011001000000 1001110111:10101101001100101011100110111111 1001111000:00111011101001000010111100101001 1001111001:11000100010110111101000011010110 1001111010:01101110111100010111101001111100 1001111011:0010001000011101000010110000011 1001111100:00001000100101110001110000011010 1001111101:11110111011010001110001111100101 1001111110:01011101110000100100100101001111 1001111111:10100010001111011011011010110000 1010000000:00011101111110100100001010010110 1010000001:1100010000001011011110101101001 1010000010:01001000101011110001011111000011 1010000011:0110111010100001110100000111100 1010000100:0101110110010010111000110100101 1010000101:1010001001101101000111001011010 1010000110:01111011100111000010010011110000 1010000111:10000100011000111101101100001111 1010001000:0010010111101010100110110011001 1010001001:1101101000010101011001001100110 1010001010:1000111101000000001100011001100 1010001011:10111000010111111110011100110011 1010001100:00100001110001100111111010101010 1010001101:1011110001110011000000101010101 1010001110:01110100100100110010101111111111 1010001111:0001011011011001101010000000000 1010010000:0011101000001010100001001101001 1010010001:11100010111110101011110110010110 1010010010:1001000010100000001011100111100 1010010011:10110111101011111110100011000011 1010010100:0101110001101100111000101011010 1010010101:1010001110010011000111010100101 1010010110:01111011011000110010010000001111 1010010111:10000100100111001101101111110000 1010011000:0010010000010100100110101100110 1010011001:11101101111101011011001010011001 1010011010:01000111010111110001100000110011 1010011011:10111000101000001110011111001100 1010011100:00100001001110010111111001010101 1010011101:1011110110001101000000110101010 1010011110:01110100011011000010101100000000 1010011111:10001011100100111101010011111111 1010100000:00011101111110101011110101101001 1010100001:1100010000001010100001010010110 1010100010:01001000101011111110100000111100 1010100011:0110111010100000001011111000011 1010100100:0101110110010011000111001011010 1010100101:1010001001101100111000110100101 1010100110:01111011100111001101101100001111 1010100111:0000100011000110010010011110000 1010101000:0010010111101011011001001100110 1010101001:1101101000010100100110110011001 1010101010:01000111101000001110011100110011 1010101011:0111000010111110001100011001100 1010101100:0100001110001101000000101010101 1010101101:11011110001110010111111010101010 1010101110:1110100100100111101010000000000 1010101111:10001011011011000010101111111111 1010110000:00011101000001011011110110010110 1010110001:1100010111110100100001001101001 1010110010:1001000010100001110100011000011 1010110011:10110111101011110001011100111100 1010110100:0101110001101101000111010100101 1010110101:1010001110010010111000101011010 1010110110:01111011011000111101101111110000 1010110111:0000100100111000010010000001111 1010111000:0010010000010101011001010011001 1010111001:11101101111101010100110101100110 1010111010:01000111010111111110011111001100 1010111011:0111000101000000001100000110011 1010111100:0100001001110011000000110101010 1010111101:11011110110001100111111001010101 1010111110:01110100011011001101010011111111 1010111111:0001011100100110010101100000000 1011000000:00110101100110011011001011100001 1011000001:1001010011001100100110100011110 1011000010:01100000110011001110011110110100 1011000011:0011111001100110001100001001011 1011000100:0000110101010101000000111010010 1011000101:11111001010101010111111000101101 1011000110:01010011111111111101010010000111 1011000111:0101100000000000010101101111000 1011001000:00111010100101101011110111101110 1011001001:1000101011010010100001000010001 1011001010:01101111110000111110100010111011 1011001011:0010000001111000001011101000100 1011001100:00001001101001011000111011011101 1011001101:1110110010110100111000100100010 1011001110:01011100111100001101101110001000 1011001111:10100011000011110010010001110111 1011010000:00110101011001101011001000011110 1011010001:1001010100110010100110111100001 1011010010:01100000001100111110011101001011 1011010011:10011111110011000001100010110100 1011010100:0000110010101011000000100101101 1011010101:11111001101010100111111011010010 1011010110:1010011000000001101010001111000 1011010111:10101100111111110010101110000111 1011011000:00111010011010011011110100010001 1011011001:1000101100101100100001011101110 1011011010:01101111001111001110100001000100 1011011011:10010000110000110001011110111011 1011011100:0001001010110101000111000100010 1011011101:11110110101001010111000111011101 1011011110:01011100000011111101101101110111 1011011111:10100011111100000010010010001000 1011100000:00110101100110010100110100011110 1011100001:11001010011001101011001011100001 1011100010:01100000110011000001100001001011 1011100011:10011111001100111110011110110100 1011100100:00000110101010100111111000101101 1011100101:11111001010101011000000111010010 1011100110:01010011111111110010101101111000 1011100111:10101100000000001101010010000111 1011101000:00111010100101100100001000010001 1011101001:11000101011010011011110111101110 1011101010:01101111110000110001011101000100 1011101011:10010000001111001110100010111011 1011101100:00001001101001010111000100100010 1011101101:11110110010110101000111011011101 1011101110:01011100111100000010010001110111 1011101111:10100011000011111101101110001000 1011110000:00110101011001100100110111100001 1011110001:11001010100110011011001000011110 1011110010:01100000001100110001100010110100 1011110011:10011111110011001110011101001011 1011110100:00000110010101010111111011010010 1011110101:11111001101010101000000100101101 1011110110:01010011000000000010101110000111 1011110111:10101100111111111101010001111000 1011111000:00111010011010010100001011101110 1011111001:11000101100101101011110100010001 1011111010:01101111001111000001011110111011 1011111011:10010000110000111110100001000100 1011111100:00001001010110100111000111011101 1011111101:11110110101001011000111000100010 1011111110:01011100000011110010010010001000 1011111111:10100011111100001101101101110111 1100000000:00010110110011100011010001111010 1100000001:11101001001100011100101110000101 1100000010:01000011100110110110000100101111 1100000011:10111100011001001001111011010000 1100000100:00100101111111010000011101001001 1100000101:11011010000000101111100010110110 1100000110:01110000101010000101001000011100 1100000111:10001111010101111010110111100011 1100001000:00011001110000010011101101110101 1100001001:11100110001111101100010010001010 1100001010:01001100100101000110111000100000 1100001011:10110011011010111001000111011111 1100001100:00101010111100100000100001000110 1100001101:11010101000011011111011110111001 1100001110:01111111101001110101110100010011 1100001111:10000000010110001010001011101100 1100010000:00010110001100010011010010000101 1100010001:11101001110011101100101101111010 1100010010:01000011011001000110000111010000 1100010011:10111100100110111001111000101111 1100010100:0100101000000100000011110110110 1100010101:11011010111111011111100001001001 1100010110:01110000010101110101001011100011 1100010111:10001111101010001010110100011100 1100011000:00011001001111100011101110001010 1100011001:11100110110000011100010001110101 1100011010:01001100011010110110111011011111 1100011011:10110011100101001001000100100000 1100011100:0101010000011010000100010111001 1100011101:11010101111100101111011101000110 1100011110:01111111010110000101110111101100 1100011111:10000000101001111010001000010011 1100100000:00010110110011101100101110000101 1100100001:11101001001100010011010001111010 1100100010:01000011100110111001111011010000 1100100011:10111100011001000110000100101111

TABLE 1e 1100100100: 00100101111111011111100010110110 1100100101:11011010000000100000011101001001 1100100110:01110000101010001010110111100011 1100100111:10001111010101110101001000011100 1100101000:00011001110000011100010010001010 1100101001:11100110001111100011101101110101 1100101010:01001100100101001001000111011111 1100101011:10110011011010110110111000100000 1100101100:00101010111100101111011110111001 1100101101:11010101000011010000100001000110 1100101110:01111111101001111010001011101100 1100101111:10000000010110000101110100010011 1100110000:00101100011000111001101101111010 1100110001:11101001110011100011010010000101 1100110010:01000011011001001001111000101111 1100110011:10111100100110110110000111010000 1100110100:00100101000000101111100001001001 1100110101:11011010111111010000011110110110 1100110110:011100000010101111010110100011100 1100110111:10001111101010000101001011100011 1100111000:00011001001111101100010001110101 1100111001:11100110110000010011101110001010 1100111010:01001100011010111001000100100000 1100111011:10110011100101000110111011011111 1100111100:00101010000011011111011101000110 1100111101:11010101111100100000100010111001 1100111110:01111111010110001010001000010011 1100111111:10000000101001110101110111101100 1101000000:00111110101011011100010000001101 1101000001:11000001010100100011101111110010 1101000010:01101011111110001001000101011000 1101000011:10010100000001110110111010100111 1101000100:00001101100111101111011100111110 1101000101:11110010011000010000100011000001 1101000110:01011000110010111010001001101011 1101000111:10100111001101000101110110010100 1101001000:00110001101000101100101100000010 1101001001:11001110010111010011010011111101 1101001010:01100100111101111001111001010111 1101001011:10011011000010000110000110101000 1101001100:00000010100100011111100000110001 1101001101:11111101011011100000011111001110 1101001110:01010111110001001010110101100100 1101001111:10101000001110110101001010011011 1101010000:00111110010100101100010011110010 1101010001:11000001101011010011101100001101 1101010010:01101011000001111001000110100111 1101010011:10010100111110000110111001011000 1101010100:00001101011000011111011111000001 1101010101:11110010100111100000100000111110 1101010110:01011000001101001010001010010100 1101010111:10100111110010110101110101101011 1101011000:00110001010111011100101111111101 1101011001:11001110101000100011010000000010 1101011010:01100100000010001001111010101000 1101011011:10011011111101110110000101010111 1101011100:00000010011011101111100011001110 1101011101:11111101100100010000011100110001 1101011110:01010111001110111010110110011011 1101011111:10101000110001000101001001100100 1101100000:00111110101011010011101111110010 1101100001:11000001010100101100010000001101 1101100010:01101011111110000110111010100111 1101100011:10010100000001111001000101011000 1101100100:00001101100111100000100011000001 1101100101:11110010011000011111011100111110 1101100110:01011000110010110101110110010100 1101100111:10100111001101001010001001101011 1101101000:00110001101000100011010011111101 1101101001:11001110010111011100101100000010 1101101010:01100100111101110110000110101000 1101101011:10011011000010001001111001010111 1101101100:00000010100100010000011111001110 1101101101:111111010110111011111000000110001 1101101110:01010111110001000101001010011011 1101101111:10101000001110111010110101100100 1101110000:00111110010100100011101100001101 1101110001:11000001101011011100010011110010 1101110010:01101011000001110110111001011000 1101110011:10010100111110001001000110100111 1101110100:00001101011000010000100000111110 1101110101:11110010100111101111011111000001 1101110110:01011000001101000101110101101011 1101110111:10100111110010111010001010010100 1101111000:00110001010111010011010000000010 1101111001:11001110101000101100101111111101 1101111010:01100100000010000110000101010111 1101111011:10011011111101111001111010101000 1101111100:00000010011011100000011100110001 1101111101:11111101100100011111100011001110 1101111110:01010111001110110101001001100100 1101111111:10101000110001001010110110011011 1110000000:00010111000000110101100110111101 1110000001:11101000111111001010011001000010 1110000010:01000010010101100000110011101000 1110000011:10111101101010011111001100010111 1110000100:00100100001100000110101010001110 1110000101:11011011110011111001010101110001 1110000110:01110001011001010011111111011011 1110000111:10001110100110101100000000100100 1110001000:00011000000011000101011010110010 1110001001:11100111111100111010100101001101 1110001010:01001101010110010000001111100111 1110001011:10110010101001101111110000011000 1110001100:00101011001111110110010110000001 1110001101:1101010011000000100110100111110 1110001110:01111110011010100011000011010100 1110001111:10000001100101011100111100101011 1110010000:0001011111111000101100101000010 1110010001:1110100000000111010011010111101 1110010010:01000010101010010000110000010111 1110010011:10111101010101101111001111101000 1110010100:00100100110011110110101001110001 1110010101:11011011001100001001010110001110 1110010110:01110001100110100011111100100100 1110010111:10001110011001011100000011011011 1110011000:00011000111100110101011001001101 1110011001:11100111000011001010100110110010 1110011010:01001101101001100000001100011000 1110011011:10110010010110011111110011100111 1110011100:00101011110000000110010101111110 1110011101:11010100001111111001101010000001 1110011110:01111110100101010011000000101011 1110011111:10000001011010101100111111010100 1110100000:00010111000000111010011001000010 1110100001:11101000111111000101100110111101 11101000010:1000010010101101111001100010111 1110100011:10111101101010010000110011101000 1110100100:00100100001100001001010101110001 1110100101:11011011110011110110101010001110 1110100110:01110001011001011100000000100100 1110100111:10001110100110100011111111011011 1110101000:00011000000011001010100101001101 1110101001:11100111111100110101011010110010 1110101010:01001101010110011111110000011000 1110101011:10110010101001100000001111100111 1110101100:00101011001111111001101001111110 1110101101:11010100110000000110010110000001 1110101110:01111110011010101100111100101011 1110101111:10000001100101010011000011010100 1110110000:00010111111111001010011010111101 1110110001:11101000000000110101100101000010 1110110010:01000010101010011111001111101000 1110110011:10111101010101100000110000010111 1110110100:00100100110011111001010110001110 1110110101:11011011001100000110101001110001 1110110110:01110001100110101100000011011011 1110110111:10001110011001010011111100100100 1110111000:00011000111100111010100110110010 1110111001:11100111000011000101011001001101 1110111010:01001101101001101111110011100111 1110111011:10110010010110010000001100011000 1110111100:00101011110000001001101010000001 1110111101:11010100001111110110010101111110 1110111110:01111110100101011100111111010100 1110111111:10000001011010100011000000101011 1111000000:00111111011000001010100111001010 1111000001:11000000100111110101011000110101 1111000010:01101010001101011111110010011111 1111000011:1001010111001010000000110110000 1111000100:00001100010100111001101011111001 1111000101:11110011101011000110010100000110 1111000110:01011001000001101100111110101100 1111000111:10100110111110010011000001010011 1111001000:00110000011011111010011011000101 1111001001:11001111100100000101100100111010 1111001010:01100101001110101111001110010000 1111001011:10011010110001010000110001101111 1111001100:00000011010111001001010111110110 1111001101:11111100101000110110101000001001 1111001110:01010110000010011100000010100011 1111001111:101010011111011000011111101011100 1111010000:00111111100111111010100100110101 1111010001:11000000011000000101011011001010 1111010010:01101010110010101111110001100000 1111010011:10010101001101010000001110011111 1111010100:00001100101011001001101000000110 1111010101:11110011010100110110010111111001 1111010110:01011001111110011100111101010011 1111010111:10100110000001100011000010101100 1111011000:00110000100100001010011000111010 1111011001:11001111011011110101100111000101 1111011010:01100101110001011111001101101111 1111011011:10011010001110100000110010010000 1111011100:00000011101000111001010100001001 1111011101:11111100010111000110101011110110 1111011110:010101101111011011000000011100 1111011111:10101001000010010011111110100011 1111100000:00111111011000000101011000110101 1111100001:11000000100111111010100111001010 1111100010:01101010001101010000001101100000 1111100011:10010101110010101111110010011111 1111100100:00001100010100110110010100000110 1111100101:11110011101011001001101011111001 1111100110:01011001000001100011000001010011 1111100111:10100110111110011100111110101100 1111101000:00110000011011110101100100111010 1111101001:11001111100100001010011011000101 1111101010:01100101001110100000110001101111 1111101011:10011010110001011111001110010000 1111101100:00000011010111000110101000001001

TABLE 1f 1111101101: 11111100101000111001010111110110 1111101110:01010110000010010011111101011100 1111101111:10101001111101101100000010100011 1111110000:00111111100111110101011011001010 1111110001:11000000011000001010100100110101 1111110010:01101010110010100000001110011111 1111110011:10010101001101011111110001100000 1111110100:00001100101011000110010111111001 1111110101:11110011010100111001101000000110 1111110110:01011001111110010011000010101100 1111110111:10100110000001101100111101010011 1111111000:00110000100100000101100111000101 1111111001:11001111011011111010011000111010 1111111010:01100101110001010000110010010000 1111111011:10011010001110101111001101101111 1111111100:00000011101000110110101011110110 1111111101:11111100010111001001010100001001 1111111110:01010110111101100011111110100011 1111111111:10101001000010011100000001011100

The decoding apparatus according to the embodiment of the presentinvention will be described referring to FIG. 9. An input signal r(t) isapplied to 15 multipliers 902 to 906 and a correlation calculator 920.The input signal r(t) was encoded with a predetermined Walsh code and apredetermined mask sequence in a transmitter. A mask sequence generator910 generates all possible 15 mask sequences M1 to M15. The multipliers902 to 906 multiply the mask sequences received from the mask sequencegenerator 910 by the input signal r(t). The multiplier 902 multipliesthe input signal r(t) by the mask sequence M1 received from the masksequence generator 910. The multiplier 904 multiplies the input signalr(t) by the mask sequence M2 received from the mask sequence generator910. The multiplier 906 multiplies the input signal r(t) by the masksequence M15 received from the mask sequence generator 910. If thetransmitter encoded TFCI bits with the predetermined mask sequence, oneof the outputs of the multipliers 902 to 906 is free of the masksequence, which means the mask sequence has no effect on thecorrelations calculated by one of the correlation calculators. Forexample, if the transmitter used the mask sequence M2 for encoding theTFCI bits, the output of the multiplier 904 that multiplies the masksequence M2 by the input signal r(t) is free of the mask sequence. Themask sequence-free signal is TFCI bits encoded with the predeterminedWalsh code. Correlation calculators 920 to 926 calculate thecorrelations of the input signal r(t) and the outputs of the multipliers902 to 906 to 64 bi-orthogonal codes. The 64 bi-orthogonal codes havebeen defined before. The correlation calculator 920 calculates thecorrelation values of the input signal r(t) to the 64 bi-orthogonalcodes of length 32, selects the maximum correlation value from the 64correlations, and outputs the selected correlation value, abi-orthogonal code index corresponding to the selected correlationvalue, and its unique index “0000” to a correlation comparator 940.

The correlation calculator 922 calculates the correlation values of theoutput of the multiplier 902 to the 64 bi-orthogonal codes, selects themaximum value of the 64 correlations, and outputs the selectedcorrelation value, a bi-orthogonal code index corresponding to theselected correlation, and its unique index “0001” to the correlationcomparator 940. The correlation calculator 924 calculates thecorrelation values of the output of the multiplier 904 to the 64bi-orthogonal codes, selects the maximum of the 64 correlation values,and outputs the selected correlation value, a bi-orthogonal code indexcorresponding to the selected correlation value, and its unique index“0010” to the correlation comparator 940. Other correlationcalculators(not shown) calculate the correlation values of the outputsof the correspondent multipliers to the 64 bi-orthogonal codes andoperate similar to the above described correlation calculators,respectively.

Finally, the correlation calculator 926 calculates the correlationvalues of the output of the multiplier 906 to the 64 bi-orthogonalcodes, selects the maximum value of the 64 correlations, and outputs theselected correlation value, a bi-orthogonal code index corresponding tothe selected correlation value, and its unique index “1111” to thecorrelation comparator 940.

The unique indexes of the correlation calculators 920 to 926 are thesame as the indexes of the mask sequences multiplied by the input signalr(t) in the multipliers 902 to 906. Table 2 lists the 15 mask indexesmultiplied in the multipliers and a mask index assigned to the case thatno mask sequence is used, by way of example. TABLE 2 mask sequence masksequence index not used 0000 M1 0001 M2 0010 M3 0011 M4 0101 M5 0101 M60110 M7 0111 M8 1000 M9 1001 M10 1010 M11 1011 M12 1100 M13 1101 M141110 M15 1111

As shown in Table 2, the correlation calculator 922, which receives thesignal which is the product of the input signal r(t) and the masksequence M1, outputs “0001” as its index. The correlation calculator926, which receives the signal which is the product of the input signalr(t) and the mask sequence M15, outputs “1111” as its index. Thecorrelation calculator 920, which receives only the input signal r(t),outputs “0000” as its index.

Meanwhile, the bi-orthogonal code indexes are expressed in a binarycode. For example, if the correlation to {overscore (W4)} which is thecomplement of W4 is the largest correlation value, a correspondingbi-orthogonal code index (a0 to a9) is “001001”.

The correlation comparator 940 compares the 16 maximum correlationvalues received from the correlation calculators 920 to 926, selects thehighest correlation value from the 16 received maximum correlationvalues, and outputs TFCI bits based on the bi-orthogonal code index andthe mask sequence index(the unique index) received from the correlationcalculator that corresponds to the highest correlation value. The TFCIbits can be determined by combining the bi-orthogonal code index and themask sequence index. For example, if the mask sequence index is that ofM4(0100) and the bi-orthogonal code index is that of {overscore(W4)}(001001), the TFCI bits(a9 to a0) are “the M4 index(0100)+the{overscore (W4)} index(001001)”. That is, the TFCI bits(a9 to a0) are“0100001001”

Assuming that the transmitter transmitted code symbols corresponding toTFCI bits (a0 to a9) “1011000010”, it can be said that the transmitterencoded the TFCI bits with {overscore (W6)} and M4 according to theafore-described encoding procedure. The receiver can determine that theinput signal r(t) is encoded with the mask sequence M4 by multiplyingthe input signal r(t) by all the mask sequences and that the inputsignal r(t) is encoded with {overscore (W6)} by calculating thecorrelations of the input signal r(t) to all the bi-orthogonal codes.Based on the above example, the fifth correlation calculator(not shown)will output the largest correlation value, the index of {overscore (W6)}(101100) and its unique index(0010). Then, the receiver outputs thedecoded TFCI bits(a0 to a9) “1011000010” by adding the index of{overscore (W6)} “101100” and the M4 index “0010”.

In the embodiment of the decoding apparatus, the input signal r(t) isprocessed in parallel according to the number of mask sequences. It canbe further contemplated that the input signal r(t) is sequentiallymultiplied by the mask sequences and the correlations of the productsare sequentially calculated in another embodiment of the decodingapparatus.

FIG. 17 illustrates another embodiment of the decoding apparatus.

Referring to FIG. 17, a memory 1720 stores an input 32-symbol signalr(t). A mask sequence generator 1710 generates 16 mask sequences thatwere used in the transmitter and outputs them sequentially. A multiplier1730 multiplies one of the 16 mask sequences received from the masksequence generator 1710 by the input signal r(t) received from thememory 1720. A correlation calculator 1740 calculates the output of themultiplier 1730 to 64 biorthogonal codes bi-orthogonal of length 32 andoutputs the maximum correlation value and the index of a biorthogonalcode corresponding to the largest correlation value to a correlationcomparator 1750. The correlation comparator 1750 stores the maximumcorrelation value and the biorthogonal code index received from thecorrelation calculator 1740, and the index of the mask sequence receivedfrom the mask sequence generator 1710.

Upon completion of above processing with the mask sequence, the memory1720 outputs the stored input signal r(t) to the multiplier 1730. Themultiplier 1730 multiplies the input signal r(t) by one of the othermask sequences. The correlation calculator 1740 calculates correlationof the output of the multiplier 1730 to the 64 biorthogonal codes oflength 32 and outputs the maximum correlation value and the index of abiorthogonal code corresponding to the maximum correlation value. Thecorrelation comparator 1750 stores the maximum correlation value, thebiorthogonal code index corresponding to the maximum correlation value,and the mask sequence index received from the mask sequence generator1710.

The above procedure is performed on all of the 16 mask sequencesgenerated from the mask sequence generator 1710. Then, 16 maximumcorrelation values the indexes of biorthogonal codes corresponding tothe maximum correlation value are stored in the correlation comparator1750. The correlation comparator 1750 compares the stored 16 correlationvalues and selects the one with the highest correlation and outputs TFCIbits by combining the indexes of the biorthogonal code and mask sequenceindex corresponding to the selected maximum correlation value. When thedecoding of the TFCI bits is completed, the input signal r(t) is deletedfrom the memory 1720 and the next input signal r(t+1) is stored.

While the correlation comparator 1750 compares the 16 maximumcorrelation values at one time in the decoding apparatus of FIG. 17,real-time correlation value comparison can be contemplated. That is, thefirst input maximum correlation value is compared with the next inputmaximum correlation value and the larger of the two correlation valuesand a mask sequence index and a biorthogonal code index corresponding tothe correlation are stored. Then, the thirdly input maximum correlationis compared with the stored correlation and the larger of the twocorrelations and a mask sequence index and a biorthogonal code indexcorresponding to the selected correlation are stored. This comparisonoperation occurs 15 times which is the number of mask sequencesgenerated from the mask sequence generator 1710. Upon completion of allthe operations, the correlation comparator 1710 output the finallystored biorthogonal index(a0 to a6) and mask sequence index(a7 to a9)and outputs the added bits as TFCI bits.

FIG. 10 is a flowchart illustrating the operation of the correlationcomparator 940 shown in FIG. 9. The correlation comparator 940 storesthe sixteen maximum correlation values, selects a highest correlationvalue out of the 16 maximum correlation values and output TFCI bitsbased on the indexes of a bi-orthogonal code and a mask sequencecorresponding to the selected highest correlation value. The sixteencorrelation values are compared, and TFCI bits are outputted based onthe indexes of a bi-orthogonal code and a mask sequence corresponding tothe highest correlation value.

Referring to FIG. 10, a maximum correlation index i is set to 1 and theindices of a maximum correlation value, a biorthogonal code, and a masksequence to be checked are set to 0s in step 1000. In step 1010, thecorrelation comparator 940 receives a 1^(st) maximum correlation value,a 1^(st) bi-orthogonal code index, and a 1^(st) mask sequence index fromthe correlation calculator 920. The correlation comparator 940 comparesthe 1^(st) maximum correlation with an the previous maximum correlationvalue in step 1020. If the 1^(st) maximum correlation is greater thanthe previous maximum correlation, the procedure goes to step 1030. Ifthe 1^(st) maximum correlation is equal to or smaller than the previousmaximum correlation, the procedure goes to step 1040. In step 1030, thecorrelation comparator 940 designates the 1^(st) maximum correlation asa final maximum correlation and stores the 1^(st) bi-orthogonal code andmask sequence indexes as final bi-orthogonal code and mask sequenceindexes. In step 1040, the correlation comparator 940 compares the indexi with the number 16 of the correlation calculators to determine whetherall 16 maximum correlations are completely compared. If i is not 16, theindex i is increased by 1 in step 1060 and the procedure returns to step1010. Then, the above procedure is repeated.

In step 1050, the correlation comparator 940 outputs the indexes of thebi-orthogonal code and the mask sequence that correspond to the finalmaximum correlation as decoded bits. The bi-orthogonal code index andthe mask sequence index corresponding to the decoded bits are thosecorresponding to the final maximum correlation among the 16 maximumcorrelation values received from the 16 correlation calculators.

3. Second Embodiment of Encoding/Decoding Apparatus and Method

The (32, 10) TFCI encoder that outputs a 32-symbol TFCI codeword in viewof 16 slots has been described in the first embodiment of the presentinvention. Recently, the IMT-2000 standard specification dictates having15 slots in one frame. Therefore, the second embodiment of the presentinvention is directed to a (30, 10) TFCI encoder that outputs a30-symbol TFCI codeword in view of 15 slots. Therefore, the secondembodiment of the present invention suggests an encoding apparatus andmethod for outputting 30 code symbols by puncturing two symbols of 32coded symbols(codeword) as generated from the (32, 10) TFCI encoder.

The encoding apparatuses according to the first and second embodimentsof the present invention are the same in configuration except thatsequences output from a one-bit generator, a basis Walsh code generator,and a basis mask sequence generator. The encoder apparatus outputs codedsymbols of length 30 with symbol #0(1^(st) symbol) and symbol#16(17^(th) symbol) are punctured in the encoding apparatus of thesecond embodiment.

Referring to FIG. 8, 10 input information bits a0 to a9 are applied tothe input of the 840 to 849. The one-bit generator 800 outputs symbols1s(length 32) to the multiplier 840. The multiplier 840 multiplies theinput information bit a0 by each 32 symbol received from the one-bitgenerator 800. The basis Walsh code generator 810 simultaneouslygenerates basis Walsh codes W1, W2, W4, W8, and W16 of length 32. Themultiplier 841 multiplies the input information bit a1 by the basisWalsh code W1 “01010101010101010101010101010101”. The multiplier 842multiplies the input information bit a2 by the basis Walsh code W2“00110011001100110011001100110011”. The multiplier 843 multiplies theinput information bit a3 by the basis Walsh code W4“00001111000011110000111100001111”. The multiplier 844 multiplies theinput information bit a4 by the basis Walsh code W8“00000000111111110000000011111111”. The multiplier 845 multiplies theinput information bit a5 by the basis Walsh code W16“00000000000000001111111111111111”.

The basis mask sequence generator 820 simultaneously generates basismask sequences M1, M2, M4, and M8 of length 32. The multiplier 846multiplies the input information bit a6 by the basis mask sequence M1“00101000011000111111000001110111”. The multiplier 847 multiplies theinput information bit a7 by the basis mask sequence M2“00000001110011010110110111000111”. The multiplier 848 multiplies theinput information bit a8 by the basis mask sequence M4“00001010111110010001101100101011”. The multiplier 849 multiplies theinput information bit a9 by the basis mask sequence M8“00011100001101110010111101010001”. The multipliers 840 to 849 functionlike switches that control the output of or the generation of the bitsfrom the one-bit generator, each of the basis Walsh codes and each ofthe basis mask sequences.

The adder 860 sums the outputs of the multipliers 840 to 849 symbol bysymbol and outputs 32 coded symbols (i.e., a TFCI codeword). Out of the32 coded symbols, two symbols will be punctured at predeterminedpositions (i.e. the symbol #0(the first symbol) and symbol #16(the17^(th) symbol) of the adder 860 output are punctured). The remaining 30symbols will become the 30 TFCI symbols. It will be easy to modify thesecond embodiment of present invention. For example, the one-bitgenerator 800, basis Walsh generator 810, basis mask sequence generator820 can generate 30 symbols which excludes the #0 and #16 symbols. Theadder 860 then adds the output of the one-bit generator 800, basis Walshgenerator 810 and basis mask sequence generator 820 bit by bit andoutput 30 encoded symbols as TFCI symbols.

FIG. 12 is a encoding method for the second embodiment of presentinvention. The flowchart illustrating the steps of the encodingapparatus according to the second embodiment of the present inventionwhen the number of slots is 15.

Referring to FIG. 12, 10 input information bits a0 to a9 are receivedand variables sum and j are set to an initial value 0 in step 1200. Instep 1210, it is determined whether j is 30. If j is not 30 in step1210, the j^(th) symbols W1(j), W2(j), W4(j), W8(j), and W16(j) of thebasis Walsh codes W1, W2, W4, W8, and W16 (each having two puncturedbits) and the j^(th) symbols M1(j), M2(j), M4(j), and M8(j) of the basismask sequences M1, M2, M4, and M8 (each having two punctured bits) arereceived in step 1220. Then, the received symbols are multiplied by theinput information bits on a symbol basis and the multiplied symbols aresummed in step 1230. In step 1240, sum indicating the achieved j^(th)code symbol is output. j is increased by 1 in step 1250 and then theprocedure returns to step 1210. Meanwhile, if j is 30 in step 1210, theencoding procedure ends.

The (30, 10) encoder outputs 1024 codewords equivalent to the codewordsof the (32, 10) encoder with symbols #0 and #16 punctured. Therefore,the total number of information can be expressed is 1024.

The output of a (30, 9) encoder is combinations of 32 Walsh codes oflength 30 obtained by puncturing symbols #0 and #16 of each of 32 Walshcodes of length 32, 32 bi-orthogonal codes obtained by adding 1 to eachsymbol of the punctured Walsh codes (by multiplying −1 to each symbol inthe case of a real number), and 8 mask sequences obtained by combiningany three of the four punctured basis mask sequences.

The output of a (30, 8) encoder is combinations of 32 Walsh codes oflength 30 obtained by puncturing #0 and #16 symbols from each of 32Walsh codes having a length 32 symbols, 32 bi-orthogonal codes obtainedby adding 1 to each symbol of the punctured Walsh codes (by multiplying−1 to each symbol in the case of a real number), and 4 mask sequencesobtained by combining any two of the four punctured basis masksequences.

The output of a (30, 7) encoder is combinations of 32 Walsh codes oflength 30 obtained by puncturing #0 and #16 symbols from each of 32Walsh codes having a length 32 symbols, 32 bi-orthogonal codes obtainedby adding I to each symbol of the punctured Walsh codes (by multiplying−1 to each symbol in the case of a real number), and one of the fourpunctured basis mask sequences.

All the above encoders for providing an extended TFCI have a minimumdistance of 10. The (30, 9), (30, 8), and (30, 7) encoders can beimplemented by blocking input and output of at least one of the fourbasis mask sequences generated from the basis mask sequence generator820 shown in FIG. 8.

The above encoders flexibly encode TFCI bits according to the number ofthe TFCI bits and has a maximized minimum distance that determinesencoding performance.

A decoding apparatus according to the second embodiment of the presentinvention is the same in configuration and operation as the decodingapparatus of the first embodiment except for different signal lengths ofthe encoded symbols. That is, after (32,10) encoding, two symbols out ofthe 32 encoded symbols are punctured, or basis Walsh codes with twopunctured symbols and basis mask sequences with two punctured symbolsare used for generating the 30 encoded symbols. Therefore, except forthe received signal r(t) which includes a signal of 30 encoded symbolsand insertion of dummy signals at the punctured positions, all decodingoperations are equal to the description of the first embodiment ofpresent invention.

As FIG. 17, this second embodiment of decoding also can be implementedby a single multiplier for multiplying the masks with r(t) and a singlecorrelation calculator for calculating correlation values ofbi-orthogonal codes.

4. Third Embodiment of Encoding/Decoding Apparatus and Method

The third embodiment of the present invention provides an encodingapparatus for blocking the output of a one-bit generator in the (30, 7),(30, 8), (30, 9) or (30, 10) (hereinafter we express (30, 7-10))encoderof the second embodiment and generating another mask sequence instead inorder to set a minimum distance to 11. The encoders refer to an encoderthat outputs a 30-symbol TFCI codeword for the input of 7, 8, 9 or 10TFCI bits.

FIG. 14 is a block diagram of a third embodiment of the encodingapparatus for encoding a TFCI in the IMT 2000 system. In the drawing, a(30, 7-10) encoder is configured to have a minimum distance of 11.

The encoding apparatus of the third embodiment is similar in structureto that of the second embodiment except that a mask sequence generator1480 for generating a basis mask sequence M16 and a switch 1470 forswitching the mask sequence generator 1480 and a one-bit generator 1400to a multiplier 1440 are further provided to the encoding apparatusaccording to the third embodiment of the present invention.

The two bit punctured basis mask sequences M1, M2, M4, M8, and M16 asused in FIG. 14 are

-   -   M1=000001011111000010110100111110    -   M2=000110001100110001111010110111    -   M4=010111100111101010000001100111    -   M8=011011001000001111011100001111    -   M16=100100011110011111000101010011

Referring to FIG. 14, when a (30, 6) encoder is used, the switch 1470switches the one-bit generator 1400 to the multiplier 1440 and blocksall the basis mask sequences generated from a basis mask sequencegenerator 1480. The multiplier 1440 multiplies the symbols from theone-bit generator 1400 with the input information bit a0, symbol bysymbol.

If a (30, 7-10) encoder is used, the switch 1470 switches the masksequence generator 1480 to the multiplier 1440 and selectively uses fourbasis mask sequences generated from a basis mask sequence generator1420. In this case, 31 mask sequences M1 to M31 can be generated bycombining 5 basis mask sequences.

The structure and operation of outputting code symbols for the inputinformation bits a0 to a9 using multipliers 1440 to 1449 are the same asthe first and second embodiments. Therefore, their description will beomitted.

As stated above, the switch 1470 switches the mask sequence generator1480 to the multiplier 1440 to use the (30, 7-10) encoder, whereas theswitch 1470 switches the one-bit generator 1400 to the multiplier 1440to use the (30, 6) encoder.

For the input of 6 information bits, the (30, 6) encoder outputs a30-symbol codeword by combining 32 Walsh codes of length 30 with 32bi-orthogonal codes obtained by inverting the Walsh codes by the use ofthe one-bit generator 1400.

For the input of 10 information bits, the (30, 10) encoder outputs a30-symbol codeword by combining 32 Walsh codes of length 30 and 32 masksequences generated using five basis mask sequences. Here, the fivebasis mask sequences are M1, M2, M4, M8, and M16, as stated above andthe basis mask sequence M16 is output from the mask sequence generator1480 that is added for the encoding apparatus according to the thirdembodiment of the present invention. Hence, 1024 codewords can beachieved from the (30, 10) encoder. The (30, 9) encoder outputs a30-symbol codeword by combining 32 Walsh codes and 16 mask sequences,for the input of 9 information bits. The 16 mask sequences are achievedby combining four of five basis mask sequences. The (30, 8) encoderoutputs a 30-symbol codeword by combining 32 Walsh codes and 8 masksequences, for the input of 8 information bits. The 8 mask sequences areobtained by combining three of five basis mask sequences. For the inputof 7 information bits, the (30, 7) encoder outputs a 30-symbol codewordby combining 32 Walsh codes of length 30 and four mask sequences. Thefour mask sequences are obtained by combining two of five basis masksequences.

All the above (30, 7-10) encoders have a minimum distance of 11 toprovide extended TFCIs. The (32, 7-10) encoders can be implemented bycontrolling use of at least one of the five basis mask sequencesgenerated from the basis mask sequence generator 1420 and the masksequence generator 1480 shown in FIG. 14.

FIG. 16 is a flowchart illustrating a third embodiment of the TFCIencoding procedure in the IMT 2000 system according to the presentinvention.

Referring to FIG. 16, 10 information bits (TFCI bits) a0 to a9 arereceived and variables sum and j are set to initial values 0s in step1600. The variable sum indicates a final code symbol output aftersymbol-basis addition and the variable j indicates the count number offinal code symbols output after the symbol-basis addition. It isdetermined whether j is 30 in step 1610 in view of the length 30 ofpunctured Walsh codes and mask sequences used for encoding. The purposeof performing step 1610 is to judge whether the input information bitsare encoded with respect to the 30 symbols of each Walsh code and the 30symbols of each mask sequence.

If j is not 30 in step 1610, which implies that encoding is notcompleted with respect to all the symbols of the Walsh codes and masksequences, the j^(th) symbols W1(j), W2(j), W4(j), W8(j), and W16(j) ofthe basis Walsh codes W1, W2, W4, W8, and W16 and the j^(th) symbolsM1(j), M2(j), M4(j), M8(j), and M16(j) of the basis mask sequences M1,M2, M4, M8, and M16 are received in step 1620. In step 1630, the inputinformation bits are multiplied by the received symbols symbol by symboland the symbol products are summed.

Step 1630 can be expressed assum=a 0·M16(j)+a 1·W1(j)+a 2·W2(j)+a 3·W4(j)+a 4·W8(j)+a 5·W16(j)+a 6·M1(j)+a 7·M2(j)+a 8·M4(j)+a 9·M8(j)   (Eq.10)

As noted from Eq.10, an intended code symbol is obtained by multiplyingeach input information bit by the symbols of a corresponding basis Walshcode or basis mask sequence and summing the products.

In step 1640, sum indicating the achieved j^(th) code symbol is output.j is increased by 1 in step 1650 and then the procedure returns to step1610. Meanwhile, if j is 30 in step 1610, the encoding procedure ends.

Now there will be given a description of the third embodiment of thedecoding apparatus referring to FIG. 15. An input signal r(t) whichincludes the 30 encoded symbols signal transmitted by a transmitter andtwo dummy symbols which have been inserted at the positions that havebeen punctured by the encoder is applied to 31 multipliers 1502 to 1506and a correlation calculator 1520. A mask sequence generator 1500generates all possible 31 mask sequences of length 32 M1 to M31. Themultipliers 1502 to 1506 multiply the mask sequences received from themask sequence generator 1500 by the input signal r(t). If a transmitterencoded TFCI bits with a predetermined mask sequence, one of the outputsof the multipliers 1502 to 1506 is free of the mask sequence, whichmeans the mask sequence has no effect on the following correlationcalculator. For example, if the transmitter used the mask sequence M31for encoding the TFCI bits, the output of the multiplier 1506 thatmultiplies the mask sequence M31 by the input signal r(t) is free of themask sequence. However, if the transmitter did not use a mask sequence,the input signal r(t) itself applied to a correlation calculator 1520 isa mask sequence-free signal. Each correlation calculators 1520 to 1526calculates the correlation values of the outputs of the multipliers 1502to 1506 with 64 bi-orthogonal codes of length 32, determines maximumcorrelation value among the 64-correlation sets, and outputs thedetermined maximum correlation values, the indexes of each bi-orthogonalcodes corresponding to the determined maximum correlation values, andeach index of the mask sequences to a correlation comparator 1540,respectively.

The correlation comparator 1540 compares the 32 maximum correlationvalues received from the correlation calculators 1520 to 1526 anddetermines the largest of the maximum correlation values as a finalmaximum correlation. Then, the correlation comparator 1540 outputs thedecoded TFCI bits transmitted by the transmitter on the basis of theindexes of the bi-orthogonal code and mask sequence corresponding to thefinal maximum correlation value. As in FIG. 17, the third embodiment ofpresent invention can be also implemented by a single multiplier formultiplying the masks with r(t) and a single correlation calculator forcalculating correlation values of bi-orthogonal codes.

As described above, the present invention provides an apparatus andmethod for encoding and decoding a basic TFCI and an extended TFCIvariably so that hardware is simplified. Another advantage is thatsupport of both basic TFCI and extended TFCI error correcting codingschemes increases service stability. Furthermore, a minimum distance, afactor that determined the performance of an encoding apparatus, islarge enough to satisfy the requirement of an IMT 2000 system, therebyensuing excellent performance.

While the invention has been shown and described with reference tocertain preferred embodiments thereof, it will be understood by thoseskilled in the art that various changes in form and details may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims.

1. A TFCI encoding apparatus in a CDMA mobile communication system,comprising: an orthogonal sequence generator for generating a pluralityof basis biorthogonal sequences; a mask sequence generator forgenerating a plurality of basis mask sequences; and an operation unitfor adding a basis biorthogonal sequence and a basis mask sequenceselected among the basis biorthogonal sequences and the basis masksequences according to TFCI bits.
 2. The TFCI encoding apparatus ofclaim 1, wherein the plurality of basis biorthogonal sequences are afirst Walsh code, a second Walsh code, a fourth Walsh code, an eighthWalsh code, a sixteenth Walsh code and an all “1” sequence whichconverts the orthogonal sequences to the biorthogonal sequences.
 3. TheTFCI encoding apparatus of claim 2, wherein the plurality ofbiorthogonal sequences are Walsh codes and bi-orthogonal complementsequences of the Walsh codes.
 4. The TFCI encoding apparatus of claim 1,wherein the mask sequence generator has a first m-sequence and a secondm-sequence which can be added together to form a Gold code, forms afirst sequence group having sequences formed by cyclically shifting thefirst m-sequence and a second sequence group having sequences formed bycyclically shifting the second m-sequence, generates and applies acolumn transposition function to the sequences in the first group toconvert the sequences in the first group to orthogonal sequences,inserts a column of ‘0’ in the front of the sequences in the secondgroup, and generates and applies a reverse column transposition functionto the sequences in the second group to convert the sequences in thesecond group to mask sequences.
 5. The TFCI encoding apparatus of claim1, wherein the basis mask sequences are a first mask sequence“00101000011000111111000001110111”, a second mask sequence“00000001110011010110110111000111”, a fourth mask sequence“00001010111110010001101100101011”, and an eighth mask sequence“00011100001101110010111101010001”.
 6. The TFCI encoding apparatus ofclaim 1, wherein the operation unit comprises: a plurality of firstmultipliers for multiplying the basis biorthogonal sequences bycorresponding TFCI bits; a plurality of second multipliers formultiplying the basis mask sequences by corresponding TFCI bits; and anadder for adding the outputs of the first and second multipliers andgenerating the sum as the TFCI sequence.
 7. The TFCI encoding apparatusof claim 6, wherein the same symbols are Is.
 8. The TFCI encodingapparatus of claim 6, wherein the plurality of basis orthogonalsequences are a first Walsh code, a second Walsh code, a fourth Walshcode, an eighth Walsh code, and a sixteenth Walsh code.
 9. An apparatusfor encoding TFCI bits including first information bits and secondinformation bits in a CDMA mobile communication system, comprising: anorthogonal sequence generator for generating a plurality of biorthogonalsequences and outputting a biorthogonal sequence selected based on thefirst information bits among the plurality of biorthogonal sequences; amask sequence generator for generating a plurality of mask sequences andoutputting a mask sequence selected based on the second information bitsamong the plurality of mask sequences; and an adder for adding thebiorthogonal sequence and the mask sequence received from the orthogonalsequence generator.
 10. The TFCI encoding apparatus of claim 9, whereinthe mask sequence generator has a first m-sequence and a secondm-sequence which can be added together to form a Gold code, forms afirst sequence group having sequences formed by cyclically shifting thefirst m-sequence and a second sequence group having sequences formed bycyclically shifting the second m-sequence, generates and applies acolumn transposition function to the sequences in the first group toconvert the sequences in the first group to orthogonal sequences,inserts a column of ‘0’ in the front of the sequences in the secondgroup, and generates and applies a reverse column transposition functionto the sequences in the second group to convert the sequences in thesecond group to the mask sequences.
 11. A TFCI encoding method in a CDMAmobile communication system, comprising the steps of: generating aplurality of basis biorthogonal sequences; generating a plurality ofbasis mask sequences; and adding a basis biorthogonal sequence and abasis mask sequence selected among the basis biorthogonal sequences andthe basis mask sequences according to TFCI bits.
 12. The TFCI encodingmethod of claim 11, wherein the plurality of basis biorthogonalsequences are a first Walsh code, a second Walsh code, a fourth Walshcode, an eighth Walsh code, a sixteenth Walsh code and an all “1”sequence which converts the orthogonal sequences to the biorthogonalsequences.
 13. The TFCI encoding apparatus of claim 11, wherein the masksequence generator has a first m-sequence and a second m-sequence whichcan be added together to form a Gold code, forms a first sequence grouphaving sequences formed by cyclically shifting the first m-sequence anda second sequence group having sequences formed by cyclically shiftingthe second m-sequence, generates and applies a column transpositionfunction to the sequences in the first group to convert the sequences inthe first group to orthogonal sequences, inserts a column of ‘0’ in thefront of the sequences in the second group, and generates and applies areverse column transposition function to the sequences in the secondgroup to convert the sequences in the second group to the masksequences.
 14. The TFCI encoding method of claim 11, wherein the basismask sequences are a first mask sequence“00101000011000111111000001110111”, a second mask sequence“00000001110011010110110111000111”, a fourth mask sequence“00001010111110010001101100101011”, and an eighth mask sequence“00011100001101110010111101010001”.
 15. The TFCI encoding method ofclaim 11, wherein the basis orthogonal sequences are multiplied bycorresponding TFCI bits, the basis mask sequences are multiplied bycorresponding TFCI bits, and the multiplication results are added to theTFCI sequence in the TFCI sequence generating step.
 16. A method ofencoding TFCI bits including first information bits and secondinformation bits in a CDMA mobile communication system, comprising thesteps of: generating a plurality of biorthogonal sequences andoutputting a biorthogonal sequence selected based on the firstinformation bits among the plurality of biorthogonal sequences;generating a plurality of mask sequences and outputting a mask sequenceselected based on the second information bits among the plurality ofmask sequences; and adding the selected biorthogonal sequence and theselected mask sequence.
 17. The TFCI encoding method of claim 16,wherein the plurality of biorthogonal sequences are Walsh codes andcomplement codes of the Walsh codes.
 18. The TFCI encoding apparatus ofclaim 16, wherein the mask sequence generator has a first m-sequence anda second m-sequence which can be added together to form a Gold code,forms a first sequence group having sequences formed by cyclicallyshifting the first m-sequence and a second sequence group havingsequences formed by cyclically shifting the second m-sequence, generatesand applies a column transposition function to the sequences in thefirst group to convert the sequences in the first group to orthogonalsequences, inserts a column of ‘0’ in the front of the sequences in thesecond group, and generates and applies a reverse column transpositionfunction to the sequences in the second group to convert the sequencesin the second group to the mask sequences.
 19. A TFCI encoding method ina CDMA mobile communication system, comprising the steps of: generatingthe same symbols; generating a plurality of basis orthogonal sequences;generating a plurality of basis mask sequences; receiving TFCI bits andmultiplying the same symbols by corresponding TFCI bits, the pluralityof basis orthogonal sequences by corresponding TFCI bits, and theplurality of basis mask sequences by corresponding TFCI bits; and addingthe multiplication results.
 20. The TFCI encoding method of claim 19,wherein the same symbols are Is.
 21. The TFCI encoding method of claim19, wherein the plurality of basis orthogonal sequences are a firstWalsh code, a second Walsh code, a fourth Walsh code, an eighth Walshcode, and a sixteenth Walsh code.
 22. The TFCI encoding apparatus ofclaim 19, wherein the mask sequence generator has a first m-sequence anda second m-sequence which can be added together to form a Gold code,forms a first sequence group having sequences formed by cyclicallyshifting the first m-sequence and a second sequence group havingsequences formed by cyclically shifting the second m-sequence, generatesand applies a column transposition function to the sequences in thefirst group to convert the sequences in the first group to theorthogonal sequences, inserts a column of ‘0’ in the front of thesequences in the second group, and generates and applies a reversecolumn transposition function to the sequences in the second group toconvert the sequences in the second group to the mask sequences.
 23. TheTFCI encoding method of claim 19, wherein the basis mask sequences are afirst mask sequence “00101000011000111111000001110111”, a second masksequence “00000001110011010110110111000111”, a fourth mask sequence“00001010111110010001101100101011”, and an eighth mask sequence“00011100001101110010111101010001”.
 24. A TFCI decoding apparatus in aCDMA mobile communication system, comprising: a mask sequence generatorfor generating at least one mask sequence; at least one operationcircuit for receiving an input signal and the generated mask sequenceand removing the mask sequences from the input signal by multiplying themask sequence by the input signal; and at least one correlator forreceiving the signal from the operation circuit, calculating correlationvalues of the received signal with a plurality of orthogonal sequencesnumbered with corresponding indexes, and selecting the largest of thecalculated correlation value and the orthogonal sequence indexcorresponding to the largest correlation value.
 25. The TFCI encodingapparatus of claim 24, wherein the mask sequence generator has a firstm-sequence and a second m-sequence which can be added together to form aGold code, forms a first sequence group having sequences formed bycyclically shifting the first m-sequence and a second sequence grouphaving sequences formed by cyclically shifting the second m-sequence,generates and applies a column transposition function to the sequencesin the first group to convert the sequences in the first group toorthogonal sequences, inserts a column of ‘0’ in the front of thesequences in the second group, and generates and applies a reversecolumn transposition function to the sequences in the second group toconvert the sequences in the second group to the mask sequences.
 26. TheTFCI decoding apparatus of claim 24, wherein the operation circuit is amultiplier.
 27. The TFCI decoding apparatus of claim 24, furthercomprising a correlation comparator for determining the largestcorrelation value received from a plurality of correlators andgenerating an orthogonal sequence index and a mask sequence indexcorresponding to the largest correlation value.
 28. The TFCI decodingapparatus of claim 27, wherein the mask sequence index is the index ofthe mask sequence used to remove a mask sequence from the input signal.29. A TFCI decoding method in a CDMA mobile communication system,comprising the steps of: generating at least one mask sequence;receiving an input signal and the mask sequence and removing a masksequence from the input signal by multiplying the mask sequence by theinput signal; receiving the product signal, calculating correlationvalues of the product signal with a plurality of orthogonal sequenceshaving corresponding indexes; and selecting the largest correlationvalue from the calculated correlation values and outputting anorthogonal sequence index corresponding to the largest correlationvalue.
 30. The TFCI encoding apparatus of claim 29, wherein the masksequence generator has a first m-sequence and a second m-sequence whichcan be added together to form a Gold code, forms a first sequence grouphaving sequences formed by cyclically shifting the first m-sequence anda second sequence group having sequences formed by cyclically shiftingthe second m-sequence, generates and applies a column transpositionfunction to the sequences in the first group to convert the sequences inthe first group to orthogonal sequences, inserts a column of ‘0’ in thefront of the sequences in the second group, and generates and applies areverse column transposition function to the sequences in the secondgroup to convert the sequences in the second group to the masksequences.
 31. The TFCI decoding method of claim 29, further comprisingthe step of determining the highest correlation value from the selectedlargest correlation values obtained by selecting the largest correlationvalue from the calculated correlation values; and outputting anorthogonal sequence index and a mask sequence index corresponding to thedetermined highest correlation value.
 32. The TFCI decoding apparatus ofclaim 31, wherein the mask sequence index is the index of the masksequence used to remove a mask sequence from the input signalcorresponding to the highest correlation value.
 33. A TFCI decodingmethod in a CDMA mobile communication system, comprising the steps of:generating a plurality of mask sequences; receiving an input signal andthe mask sequences and removing a mask sequence from the input signal bymultiplying the mask sequences by the input signal; receiving theproduct signals, calculating correlation values of each of the productsignals with a plurality of orthogonal sequences having correspondingindexes, and selecting the largest correlation values and orthogonalsequence indexes corresponding to the largest correlation values; anddetermining the highest correlation value from the largest correlationvalues and outputting an orthogonal sequence index and a mask sequenceindex corresponding to the determined highest correlation value.
 34. TheTFCI encoding apparatus of claim 33, wherein the mask sequence generatorhas a first m-sequence and a second m-sequence which can be addedtogether to form a Gold code, forms a first sequence group havingsequences formed by cyclically shifting the first m-sequence and asecond sequence group having sequences formed by cyclically shifting thesecond m-sequence, generates and applies a column transposition functionto the sequences in the first group to convert the sequences in thefirst group to orthogonal sequences, inserts a column of ‘0’ in thefront of the sequences in the second group, and generates and applies areverse column transposition function to the sequences in the secondgroup to convert the sequences in the second group to the masksequences.
 35. The TFCI decoding method of claim 33, wherein the masksequence index is the index of the mask sequence used to remove a masksequence from the input signal corresponding to the highest correlationvalue.
 36. A TFCI decoding method in a CDMA mobile communication system,comprising the steps of: generating a plurality of mask sequences;receiving an input signal and the mask sequences and multiplying eachmask sequence by the input signal; receiving the multiplied signals andcalculating correlation values of each of the received multipliedsignals with a plurality of orthogonal sequences having correspondingindexes; selecting the largest correlation value among the calculatedcorrelation values for each of the multiplied signals and an orthogonalsequence index corresponding to the largest correlation value; and;determining the highest correlation value from all of the largestcorrelation values and an orthogonal code index corresponding to thehighest correlation value.
 37. The TFCI encoding apparatus of claim 36,wherein the mask sequence generator has a first m-sequence and a secondm-sequence which can be added together to form a Gold code, forms afirst sequence group having sequences formed by cyclically shifting thefirst m-sequence and a second sequence group having sequences formed bycyclically shifting the second m-sequence, generates and applies acolumn transposition function to the sequences in the first group toconvert the sequences in the first group to orthogonal sequences,inserts a column of ‘0’ in the front of the sequences in the secondgroup, and generates and applies a reverse column transposition functionto the sequences in the second group to convert the sequences in thesecond group to the mask sequences.
 38. The TFCI decoding method ofclaim 26, wherein the mask sequence index is the index of the masksequence used to remove a mask sequence from the input signalcorresponding to the highest correlation value.